Dynamical systems with applications using mathematica®

Dynamical Systems with Applications using Mathematica®

Volumn , Issue , 2007, Pages 1-484

  Lynch, Stephen ^a  

^a MANCHESTER METROPOLITAN UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84892821511     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-0-8176-4586-1     Document Type: Book

References (525)

1. B. Bhattacharya and M. Majumdar, Random Dynamical Systems: Theory and Applications, Cambridge University Press, Cambridge, UK, 2007.
2. J. Chiasson and J. J. Loiseau, Applications of Time Delay Systems, Springer-Verlag, New York, 2007.
3. V. Volterra, Theory of Functionals and of Integral and Integro-Differential Equations, Dover, New York, 2005.
4. J. K. Hale, L. T. Magalhaes, and W. Oliva, Dynamics in Infinite Dimensions, 2nd ed., Springer-Verlag, New York, 2002.
5. S. Wolfram, The Mathematica Book, 6th ed. (electronic), Wolfram Media, Champaign, IL, 2007; included with Mathematica® Version 6.0.
6. D. McMahon and D. M. Topa, A Beginner's Guideto Mathematica, Chapman and Hall, London, CA, 2006.
7. G. Baumann, Mathematica for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics, Springer-Verlag, New York, 2005.
8. G. Baumann, Mathematica for Theoretical Physics: Electrodynamics, Quantum Mechanics, General Relativity, and Fractals, Springer-Verlag, New York, 2005.
9. M. Trott, The Mathematica Guidebook for Numerics, Springer-Verlag, New York, 2005.
10. M. Trott, The Mathematica Guidebook for Symbolics, Springer-Verlag, New York, 2005.
11. M. Trott, The Mathematica Guidebook: Graphics, Springer-Verlag, New York, 2004.
12. M. Trott, The Mathematica Guidebook: Programming, Springer-Verlag, New York, 2004.
13. E. Don, Schaum's Outline of Mathematica, McGraw-Hill, New York, 2000.
14. B. Rai and D. P. Choudhury, Elementary Ordinary Differential Equations, Alpha Science International, Oxford, UK, 2005.
15. M. L. Abell and J. P. Braselton, Differential Equations with Mathematica, 3rd ed., Academic Press, New York, 2004.
16. S. G. Krantz, Differential Equations Demystified, McGraw-Hill, New York, 2004.
17. C. C. Ross, Differential Equations: An Introduction with Mathematica, Springer-Verlag, New York, 2004.
18. D. Richards, Advanced Mathematical Methods with Mathematica, Cambridge University Press, Cambridge, UK, 2001.
19. G. Turrell, Mathematics for Chemistry and Physics, Academic Press, New York, 2001.
20. D. G. Zill, A First Course in Differential Equations with Modeling Applications, Brooks-Cole, Belmont, CA, 2000.
21. M. R. Spiegel, Schaum's Outline of Laplace Transforms, McGraw-Hill, New York, 1965.
22. R. Bronson and G. Costa, Schaum's Outline of Differential Equations, 3rd ed., McGraw-Hill, New York, 2006.
23. J. C. Robinson, An Introduction to Ordinary Differential Equations, Cambridge University Press, Cambridge, UK, 2004.
24. W. Kelley and A. Peterson, The Theory of Differential Equations: Classical and Qualitative, Prentice-Hall, Upper Saddle River, NJ, 2003.
25. A. C. King, J. Billingham, and S. R. Otto, Differential Equations: Linear, Nonlinear, Ordinary, Partial, Cambridge University Press, Cambridge, UK, 2003.
26. J. H. Liu, A First Course in the Qualitative Theory of Differential Equations, Prentice-Hall, Upper Saddle River, NJ, 2002.
27. D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, 3rd ed., Oxford University Press, Oxford, UK, 1999.
28. B. West, S. Strogatz, J. M. McDill, J. Cantwell, and H. Hohn, Interactive Differential Equations, Version 2.0, Addison-Wesley, Reading, MA, 1997.
29. P. Hartman, Ordinary Differential Equations, Wiley, New York, 1964.
30. S. R. Hall, M. A. Duffy, and C. E. Cáceres, Selective predation and productivity jointly drive complex behavior in host-parasite systems, Amer. Naturalist, 165-1(2005), 70-81.
31. A. Hastings, Population Biology: Concepts and Models, Springer-Verlag, New York, 2005.
32. H. R. Thieme, Mathematics in Population Biology, Princeton Series in Theoretical and Computational Biology, Princeton University Press, Princeton, NJ, 2003.
33. F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, New York, 2001.
34. Y. Lenbury S. Rattanamongkonkul, N. Tumrasvin, and S. Amornsamankul, Predator-prey interaction coupled by parasitic infection: Limit cycles and chaotic behaviour, Math. Comput. Model., 30-9-10(1999), 131-146.
35. S. B. Hsu and T. W. Hwang, Hopf bifurcation analysis for a predator-prey system of Holling and Leslie type, Taiwan J. Math., 3(1999), 35-53.
36. V. Volterra, Variazioni e fluttuazioni del numero d'individui in specie animali conviventi, Mem. R. Accad. Naz. Lincei, 2-3(1926), 30-111;
37. Mem. R. Com. Tolassogr. Ital., 431(1927), 1-142.
38. A. J. Lotka, Elements of Physical Biology, William and Wilkins, Baltimore, 1925.
39. L. Perko, Differential Equations and Dynamical Systems, 3rd ed., Springer-Verlag, Berlin, New York, Heidelberg, 2006.
40. B. Shivamoggi, Perturbation Methods for Differential Equations, Birkhäuser Boston, Cambridge, MA, 2006.
41. M. S. Padin, F. I. Robbio, J. L. Moiola, and G. R. Chen, On limit cycle approximations in the van der Pol oscillator, Chaos Solitons Fractals, 23(2005), 207-220
42. D. B. Owens, F. J. Capone, R. M. Hall, J. M. Brandon, and J. R. Chambers, Transonic free-to-roll analysis of abrupt wing stall on military aircraft, J. Aircraft, 41-3(2004), 474-484.
43. E. J. Hinch, Perturbation Methods, Cambridge University Press, Cambridge, UK, 2002.
44. A. Agarwal and N. Ananthkrishnan, Bifurcation analysis for onset and cessation of surge in axial flow compressors, Internat. J. Turbo Jet Engines, 17-3(2000), 207-217.
45. A. H. Nayfeh, Perturbation Methods, Wiley-Interscience, New York, 2000.
46. C. C. Rocsoreanu, A. Georgeson, and N. Giurgiteanu, The Fitzhugh-Nagumo Model: Bifurcation and Dynamics, Kluwer, Dordrecht, Netherlands, 2000.
47. J. A. Yorke, contributor, K. Alligood, ed., and T. Sauer, ed., Chaos: An Introduction to Dynamical Systems, Springer-Verlag, New York, 1996.
48. A. L. Hodgkin and A. F. Huxley, A qualitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol., 117(1952), 500-544;
49. reproduced in Bull. Math. Biol., 52(1990), 25-71.
50. Ye Yan Qian, Theory of Limit Cycles, Translations of Mathematical Monographs, Vol. 66, American Mathematical Society, Providence, RI, 1986.
51. J. Nagumo, S. Arimoto, and S. Yoshizawa, An active pulse transmission line simulating 1214-nerve axons, Proc. IRL, 50(1970), 2061-2070.
52. R. Fitzhugh, Impulses and physiological states in theoretical models of nerve membranes, J. Biophys., 1182(1961), 445-466.
53. J. Rayleigh, The Theory of Sound, Dover, New York, 1945.
54. A. Liénard, Étude des oscillations entrenues, Rev. Gén. Électricité, 23(1928), 946-954.
55. B. Van Der Pol, On relaxation oscillations, Philos. Magazine, 7(1926), 901-912, 946-954.
56. A. V. Bolsinov and A. T. Fomenko, Integrable Hamiltonian Systems: Geometry, Topology, Classification, CRC Press, Boca Raton, FL, 2004.
57. R. L. Devaney, M. Hirsch, and S. Smale, Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2nd ed., Academic Press, New York, 2003.
58. A. Bacciotti and L. Rosier, Liapunov Functions and Stability in Control Theory, Springer-Verlag, New York, 2001.
59. G. M. Zaslavsky, Physics of Chaos in Hamiltonian Systems, World Scientific, Singapore, 1998.
60. J. Moser, Recent developments in the theory of Hamiltonian systems, SIAM Rev., 28-4(1986), 459-485.
61. J. P. Lasalle, Stability by Liapunov's Direct Method: With Applications, Academic Press, New York, 1961.
62. V. V. Nemitskii and V. V. Stepanov, Qualitative Theory of Differential Equations, Princeton University Press, Princeton, NJ, 1960
63. A. D. Bruno and V. F. Edneral, Normal forms and integrability of ODE systems, in Computer Algebrain Scientific Computing: Proceedings, Lecture Notes in Computer Science, Vol. 3718, Springer-Verlag, New York, 2005, 65-74.
64. J. Murdock, Normal Forms and Unfoldings for Local Dynamical Systems, Springer-Verlag, New York, 2003.
65. K. Ikeda and M. Murota, Imperfect Bifurcations in Structures and Materials, Springer-Verlag, New York, 2002.
66. J. M. T. Thompson and H. B. Stewart, Nonlinear Dynamics and Chaos, 2nd ed., Wiley, New York, 2002.
67. S. H. Strogatz, Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering, Perseus Books, New York, 2001.
68. M. Demazure and D. Chillingworth (translator), Bifurcations and Catastrophes: Chemistry and Engineering, Springer-Verlag, New York, 2001.
69. S. Lynch and C. J. Christopher, Limit cycles in highly nonlinear differential equations, J. Sound Vibration, 224-3(1999), 505-517.
70. G. Iooss and D. D. Joseph, Elementary Stability and Bifurcation Theory, Springer-Verlag, Berlin, New York, Heidelberg, 1997.
71. R. Seydel, Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos, Springer-Verlag, Berlin, New York, Heidelberg, 1994.
72. A. H. Nayfeh, Method of Normal Forms, Wiley Series in Nonlinear Science, Wiley, New York, 1993.
73. D. K. Arrowsmith and C. M. Place, An Introduction to Dynamical Systems, Cambridge University Press, Cambridge, UK, 1990.
74. B. Krauskopf, H. M. Osinga, E. J. Doedel, M. E. Henderson, J. M. Guckenheimer, A. Vladimirsky, M. Dellnitz, and O. Junge, A survey of methods for computing (un) stable manifolds of vector fields, Internat. J. Bifurcation Chaos, 15-3(2005), 763-791.
75. P. Zhou, X. H. Luo, and H. Y. Chen, Anew chaotic circuit and its experimental results, Acta Phys. Sinica, 54-11(2005), 5048-5052.
76. G. A. Gottwald and I. Melbourne, A new test for chaos in deterministic systems, Proc. Roy. Soc. London A, 460-2042(2004), 603-611.
77. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, Berlin, New York, Heidelberg, 1990
78. J. Borresen and S. Lynch, Further investigation of hysteresis in Chua's circuit, Internat. J. Bifurcation Chaos, 12(2002), 129-134.
79. R. C. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, 2nd ed., Oxford University Press, Oxford, UK, 2000.
80. M. Zoltowski, An adaptive reconstruction of chaotic attractors out of their single trajectories, Signal Process., 80-6(2000), 1099-1113.
81. N. Arnold, Chemical Chaos, Hippo, London, 1997.
82. S. Ellner and P. Turchin, Chaos in a noisy world: New methods and evidence from time-series analysis, Amer. Naturalist, 145-3(1995), 343-375.
83. S. K. Scott, Oscillations, Waves, and Chaos in Chemical Kinetics, Oxford Science Publications, Oxford, UK, 1994.
84. R. N. Madan, Chua's Circuit: A Paradigm for Chaos, World Scientific, Singapore, 1993.
85. M. T. Rosenstein, J. J. Collins, and C. J. Deluca, A practical method for calculating largest Lyapunov exponents from small data sets, Phys. D, 65-1-2(1993), 117-134.
86. K. Geist, U. Parlitz, and W. Lauterborn, Comparison of different methods for computing Lyapunov exponents, Progr. Theoret. Phys., 83(1990), 875-893.
87. J. P. Eckmann, S. O. Kamphorst, D. Ruelle, and S. Ciliberto, Liapunov exponents from time series, Phys. Rev. A, 34-6(1986), 4971-4979.
88. R. Field and M. Burger, eds., Oscillations and Travelling Waves in Chemical Systems, Wiley, New York, 1985.
89. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, Determining Lyapunov exponents from a time series, Phys. D, 16(1985), 285-317.
90. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, Springer-Verlag, New York, 1982.
91. O. E. Rössler, An equation for continuous chaos, Phys. Lett., 57A (1976), 397-398.
92. E. N. Lorenz, Deterministic non-periodic flow, J. Atmos. Sci., 20(1963), 130-141
93. S. S. Abdullaev, Construction of Mappings for Hamiltonian Systems and Their Applications, Lecture Notes in Physics, Springer-Verlag, New York, 2006.
94. S. Lynch, Dynmical Systems with Applications Using Maple, Birkhaüser Boston, Cambridge, MA, 2001.
95. C-ODE-E (Consortium for ODE Experiments), ODE Architect: The Ultimate ODE Power Tool, Wiley, New York, 1999.
96. E. S. Cheb-Terrab and H. P. De Oliveira, Poincaré sections of Hamiltonian systems, Comput. Phys. Comm., 95(1996), 171.
97. P. Pokorny, I. Schreiber, and M. Marek, On the route to strangeness without chaos in the quasiperiodically forced van der Pol oscillator, Chaos Solitons Fractals, 7(1996), 409-424.
98. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 3rd ed., Springer-Verlag, New York, 1990.
99. S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73(1967), 747-817.
100. H. Poincaré, Mémoire sur les courbes définies par une equation différentielle, J. Math., 7(1881), 375-422;
101. oeuvre, Gauthier-Villars, Paris, 1890.
102. D. M. Wang and Z. Zheng, eds., Differential Equations with Symbolic Computation, Birkhäuser, Basel, Cambridge, MA, 2005.
103. D. M. Wang, Elimination Practice: Software Tools and Applications, Imperial College Press, London, 2004.
104. H. Broer, I. Hoveijn, G. Lunter, and G. Vegter, Bifurcations in Hamiltonian Systems: Computing Singularities by Gröbner Bases, Lecture Notes in Mathematics, Springer-Verlag, New York, 2003.
105. N. Lauritzen, Concrete Abstract Algebra: From Numbers to Gröbner Bases, Cambridge University Press, Cambridge, UK, 2003.
106. D. M. Wang, Polynomial systems from certain differential equations, J. Symbolic Comput., 28(1999), 303-315.
107. B. Buchberger, ed., Gröbner Bases and Applications, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, UK, 1998.
108. T. R. Blows and L. M. Perko, Bifurcation of limit cycles from centres and separatrix cycles of planar analytic systems, SIAM Rev., 36(1994), 341-376.
109. N. G. Lloyd and S. Lynch, Small-amplitude limit cycles of certain Liénard systems, Proc. Roy. Soc. London Ser. A, 418(1988), 199-208.
110. N. G. Lloyd, Limit cycles of polynomial systems, in T. Bedford and J. Swift, eds., New Directions in Dynamical Systems, London Mathematical Society Lecture Notes Series, Vol. 127, Cambridge University Press, Cambridge, UK, 1988.
111. B. Buchberger, On Finding a Vector Space Basis of the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal, Ph. D. thesis, University of Innsbruck, Innsbruck, Austria, 1965 (in German).
112. F. Dumortier, D. Panazzolo, and R. Roussarie, More limit cycles than expected in Liénard equations, Proc. Amer. Math. Soc., 135-6(2007), 1895-1904.
113. J. Jiang, H. Maoan, Y. Pei, and S. Lynch, Limit cycles in two types of symmetric Liénard systems, Internat. J. Bifurcation Chaos, 17-6(2007), 2169-2174.
114. A. Marasco and C. Tenneriello, Periodic solutions of a 2D-autonomous system using Mathematica, Math. Comput. Model., 45-5-6(2007), 681-693.
115. Y. Pei and H. Maoan, Twelve limit cycles in a cubic case of the 16th Hilbert problem, Internat. J. Bifurcation Chaos, 15(2005), 2191-2205.
116. J. Li, Hilbert's sixteenth problem and bifurcations of planar polynomial vector fields, Internat. J. Bifurcation Chaos, 13(2003), 47-106.
117. Y. Il'yashenko, Centennial history of Hilbert's 16th problem, Bull. Amer. Math. Soc., 39(2002), 301-354.
118. C. J. Christopher and S. Lynch, Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces, Nonlinearity, 12(1999), 1099-1112.
119. H. Giacomini and S. Neukirch, Improving a method for the study of limit cycles of the Liénard equation, Phys. Rev. E, 57(1998), 6573-6576.
120. F. Dumortier and L. Chengzhi, Quadratic Liénard equations with quadratic damping, J. Differential Equations, 139(1997), 41-59.
121. F. Dumortier and L. Chengzhi, On the uniquenessof limit cycles surrounding one or more singularities for Liénard equations, Nonlinearity, 9(1996), 1489-1500.
122. C. J. Christopher and N. G. Lloyd, Small-amplitude limit cycles in polynomial Liénard systems, Nonlinear Differential Equations Appl., 3(1996), 183-190.
123. C. J. Christopher and N. G. Lloyd, Polynomial systems: A lower bound for the Hilbert numbers, Proc. Roy. Soc. London Ser. A, 450(1995), 219-224.
124. H. Zoladek, Eleven small limit cycles in a cubic vector field, Nonlinearity, 8(1995), 843-860.
125. T. R. Blows and C. Rousseau, Bifurcation at infinity in polynomial vector fields, J. Differential Equations, 104(1993), 215-242.
126. Zhang Zhifen, Ding Tongren, Huang Wenzao, and Dong Zhenxi, Qualitative Theory of Differential Equations, Translation of Mathematical Monographs, Vol. 102, American Mathematical Society, Providence, RI, 1992.
127. H. N. Moreira, Liénard-type equations and the epidemiology of maleria, Ecological Model, 60(1992), 139-150.
128. Yu. S. Il'yashenko, Finiteness Theorems for Limit Cycles, Translations of Mathematical Monographs, Vol. 94, American Mathematical Society, Providence, RI, 1991.
129. W. A. Coppel, Some quadratic systems with at most one limit cycle, in U. Kirchgraber and H. O. Walther, eds., Dynamics Reported, Vol. 2, Wiley/Teubner, New York, Stuttgart, 1988, 61-68.
130. J. Ecalle, J. Martinet, J. Moussu, and J. P. Ramis, Non-accumulation des cycles-limites I, C. R. Acad. Sci. Paris Sér. I Math., 304(1987), 375-377.
131. Li Jibin and Li Chunfu, Global bifurcation of planar disturbed Hamiltonian systems and distributions of limit cycles of cubic systems, Acta Math. Sinica, 28(1985), 509-521.
132. T. R. Blows and N. G. Lloyd, The number of small-amplitude limit cycles of Liénard equations, Math. Proc. Cambridge Philos. Soc, 95(1984), 359-366.
133. Shi Songling, A concrete example of the existence of four limit cycles for plane quadratic systems, Sci. Sinica A, 23(1980), 153-158.
134. A. Lins, W. De Melo, and C. Pugh, On Liénards equation with linear damping, in J. Palis and M. do Carno, eds., Geometry and Topology, Lecture Notes in Mathematics, Vol. 597, Springer-Verlag, Berlin, 1977, 335-357.
135. L. A. Cherkas, Conditions for a Liénard equation to have a centre, Differentsial'nye Uravneniya, 12(1976), 201-206.
136. G. S. Rychkov, The maximum number of limit cycles of the system x = y - a 0x - a1x - a2x, y = -x is two, Differentsial'nye Uravneniya, 11(1973), 380-391.
137. K. S. Sibirskii, The number of limit cycles in the neighbourhood of a critical point, Differential Equations, 1(1965), 36-47.
138. N. Bautin, On the number of limit cycles which appear with the variation of the coefficients from an equilibrium point of focus or centre type, Amer. Math. Soc. Trans., 5(1962), 396-414.
139. E. Chambon-Dubreuil, P. Auger, J. M. Gaillard, and M. Khaladi, Effect of aggressive behaviour on age-structured population dynamics, Ecological Model., 193(2006), 777-786.
140. H. Anton and C. Rorres, Elementary Linear Algebra, Wiley, NewYork, 2005.
141. V. N. Lopatin and S. V. Rosolovsky, Evaluation of the state and productivity of moose populations using Leslie matrix analyses, Alces, Suppl. 2(2002), 77-80.
142. M. R. S. Kulenovic and O. Merino, Discrete Dynamical Systems and Differential Equations with Mathematica, Chapman and Hall, London, 2002.
143. S. Barnet, Discrete Mathematics, Addison-Wesley, Reading, MA, 1998.
144. S. Jal and T. G. Hallam, Effects of delay, truncations and density dependence in reproduction schedules on stability of nonlinear Leslie matrix models, J. Math. Biol., 31-4(1993), 367-395
145. S. Lynch and Z. G. Bandar, Bistable neuromodules, Nonlinear Anal. Theory Methods Appl., 63(2005), 669-677.
146. S. Lynch, Analysis of a blood cell population model, Internat. J. Bifurcation Chaos, 15(2005), 2311-2316.
147. E. Ahmed, A. El-Misiery, and H. N. Agiza, On controlling chaos in an inflation-unemployment dynamical system, Chaos Solitons Fractals, 10-9(1999), 1567-1570
148. F. Paseman and N. Stollenwerk, Attractor switching by neural control of chaotic neurodynamics, Comput. Neural Systems, 9(1998), 549-561.
149. H. Nagashima and Y. Baba, Introduction to Chaos: Physics and Mathematics of Chaotic Phenomena, Institute of Physics, Bristol, PA, 1999.
150. R. A. Holmgrem, A First Course in Discrete Dynamical Systems, Springer-Verlag, Berlin, New York, Heidelberg, 1996.
151. D. Kaplan and L. Glass, Understanding Nonlinear Dynamics, Springer-Verlag, Berlin, New York, Heidelberg, 1995.
152. S. M. Hammel, C. K. R. T. Jones, and J. V. Moloney, Global dynamical behavior of the optical field in a ring cavity, J. Optical Soc. Amer. B, 2-4(1985), 552-564.
153. R. H. Day, Irregular growth cycles, Amer. Econ. Rev., 72(1982), 406-414.
154. A. Lasota, Ergodic problems in biology, in Dynamical Systems, Vol. 2: Wa r - saw, Astérisque, Vol. 50, Société Mathématique de France, Paris, 1977, 239-250.
155. T. Y. Li and J. A. Yorke, Period three implies chaos, Amer. Math. Monthly, 82(1975), 985-992.
156. R. M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton, NJ, 1974.
157. M. Hénon, Numerical study of quadratic area-preserving mappings, Quart. Appl. Math., 27(1969), 291-311
158. B. B. Mandelbrot and R. L. Hudson, The (Mis) Behavior of Markets: A Fractal View of Risk, Ruin And Reward, Perseus Books, New York, 2006.
159. R. L. Devaney and L. Keen, eds., Complex Dynamics: Twenty-Five Years After the Appearance of the Mandelbrot Set, Contemporary Mathematics, American Mathematical Society, Providence, RI, 2005.
160. R. L. Devaney, The Mandelbrot Set and Julia Sets: A Toolkit of Dynamics Activities, Key Curriculum Press, Emeryville, CA, 2002.
161. G. W. Flake, The Computational Beauty of Nature: Computer Explorations of Fractals, MIT Press, Cambridge, MA, 1998.
162. H.-O. Peitgen, ed., E. M. Maletsky, H. Jürgens, T. Perciante, D. Saupe, and L. Yunker, Fractals for the Classroom: Strategic Activities, Vol. 2, Springer-Verlag, New York, 1993.
163. H.-O. Peitgen, H. Jürgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer-Verlag, New York, 1992.
164. H.-O. Peitgen, H. Jürgens, D. Saupe, and C. Zahlten, Fractals: An Animated Discussion, Spektrum Akademischer Verlag, Heidelberg, 1989;
165. W. H. Freeman, New York, 1990.
166. H.-O. Peitgen and P. H. Richter, The Beauty of Fractals, Springer-Verlag, Berlin, New York, Heidelberg, 1986.
167. P. Mandel, Theoretical Problems in Cavity Nonlinear Optics, Cambridge University Press, Cambridge, UK, 2005.
168. T. Schneider, Nonlinear Optics in Telecommunications, Springer-Verlag, New York, 2004.
169. G. P. Agrawal, Nonlinear Fibre Optics, 3rd ed., Academic Press, New York, London, 2001.
170. G. P. Agrawal, Applications in Nonlinear Fiber Optics, Academic Press, New York, London, 2001.
171. R. Matthews, Catch the wave, New Scientist, 162-2189(1999), 27-32.
172. H. Li and K. Ogusu, Analysis of optical instability in a double-coupler nonlinear fibre ring resonator, Optics Comm., 157(1998), 27-32.
173. S. Lynch, A. L. Steele, and J. E. Hoad, Stability analysis of nonlinear optical resonators, Chaos Solitons Fractals, 9-6(1998), 935-946.
174. K. Ogusu, A. L. Steele, J. E. Hoad, and S. Lynch, Corrections to and comments on "Dynamic behaviour of reflection optical bistability in a nonlinear fibre ring resonator", IEEE J. Quantum Electron., 33(1997), 2128-2129.
175. A. L. Steele, S. Lynch, and J. E. Hoad, Analysis of optical instabilities and bistability in a nonlinear optical fibre loop mirror with feedback, Optics Comm., 137(1997), 136-142.
176. Y. H. Ja, Multiple bistability in an optical-fibre double-ring resonator utilizing the Kerr effect, IEEE J. Quantum Electron., 30-2(1994), 329-333.
177. Chao-Xiang Shi, Nonlinear fibre loop mirror with optical feedback, Optics Comm., 107(1994), 276-280.
178. N. J. Doran and D. Wood, Nonlinear-optical loop mirror, Optics Lett., 13(1988), 56-58.
179. H. M. Gibbs, Optical Bistability: Controlling Light with Light, Academic Press, New York, London, 1985.
180. S. D. Smith, Towards the optical computer, Nature, 307(1984), 315-316.
181. H. Natsuka, S. Asaka, H. Itoh, K. Ikeda, and M. Matouka, Observation of bifurcation to chaos in an all-optical bistable system, Phys. Rev. Lett., 50(1983), 109-112.
182. W. J. Firth, Stability of nonlinear Fabry-Perot resonators, Optics Comm., 39-5(1981), 343-346.
183. K. Ikeda, H. Daido, and O. Akimoto, Optical turbulence: Chaotic behaviour of transmitted light froma ring cavity, Phys. Rev. Lett., 45-9(1980), 709-712.
184. P. W. Smith and E. H. Turner, A bistable Fabry-Perot resonator, Appl. Phys. Lett., 30(1977), 280-281.
185. T. Bischofberger and Y. R. Shen, Theoretical and experimental study of the dynamic behaviour of a nonlinear Fabry-Perot interferometer, Phys. Rev. A, 19(1979), 1169-1176.
186. J. H. Marburger and F. S. Felber, Theory of a lossless nonlinear Fabry-Perot interferometer, Phys. Rev. A, 17(1978), 335-342.
187. F. S. Felber and J. H. Marburger, Theory of nonresonant multistable optical devices, Appl. Phys. Lett., 28(1976), 731.
188. A. Szöke, V. Daneu, J. Goldhar, and N. A. Kurnit, Bistable optical element and its applications, Appl. Phys. Lett., 15(1969), 376.
189. S. L. Mills, G. C. Lees, C. M. Liauw, R. N. Rothon and S. Lynch, Prediction of physical properties following the dispersion assessment of flame retardant filler/polymer composites based on the multifractal analysis of SEM images, J. Macromolecular Sci. B Phys., 44-6(2005), 1137-1151.
190. S. L. Mills, G. C. Lees, C. M. Liauw, and S. Lynch, An improved method for the dispersion assessment of flame retardent filler/polymer systems based on the multifractal analysis of SEM images, Macromolecular Materials Engrg., 289-10(2004), 864-871.
191. K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Wiley, New York, 2003.
192. D. Harte, Multifractals: Theory and Applications, Chapman and Hall, London, 2001.
193. M. Alber and J. Peinke, Improved multifractal box-counting algorithm, virtual phase transitions, and negative dimensions, Phys. Rev. E, 57-5(1998), 5489-5493.
194. K. J. Falconer and B. Lammering, Fractal properties of generalized Sierpiński triangles, Fractals, 6-1(1998), 31-41.
195. P. S. Addison, Fractals and Chaos: An Illustrated Course, Institute of Physics, Bristol, PA, 1997.
196. Li Hua, D. Ze-jun, and Wu Ziqin, Multifractal analysis of the spatial distribution of secondary-electron emission sites, Phys. Rev. B, 53-24(1996), 16631-16636.
197. V. Silberschmidt, Fractal and multifractal characteristics of propagating cracks, J. Phys. IV, 6(1996), 287-294.
198. R. M. Crownover, Introduction to Fractals and Chaos, Jones and Bartlett, Sudbury, MA, 1995.
199. J. Mach, F. Mas, and F. Sagués, Two representations in multifractal analysis, J. Phys. A, 28(1995), 5607-5622.
200. J. Muller, O. K. Huseby, and A. Saucier, Influence of multifractal scaling of pore geometry on permeabilities of sedimentary rocks, Chaos Solitons Fractals, 5-8(1995), 1485-1492.
201. N. Sarkar and B. B. Chaudhuri, Multifractal and generalized dimensions of gray-tone digital images, Signal Process., 42(1995), 181-190.
202. S. Blacher, F. Brouers, R. Fayt, and P. Teyssié, Multifractal analysis: A new method for the characterization of the morphology of multicomponent polymer systems, J. Polymer Sci. B, 31(1993), 655-662.
203. H.-O. Peitgen, H. Jürgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer-Verlag, New York, 1992.
204. H. A. Lauwerier, Fractals: Images of Chaos, Penguin, New York, 1991.
205. H.-O. Peitgen, ed., E. M. Maletsky, H. Jürgens, T. Perciante, D. Saupe, and L. Yunker, Fractals for the Classroom: Strategic Activities, #Vol. 1, Springer-Verlag, New York, 1991.
206. A. B. Chhabra, C. Meneveau, R. V. Jensen, and K. R. Sreenivasan, Direct determination of the f (a) singularity spectrum and its application to fully developed turbulence, Phys. Rev. A, 40-9(1989), 5284-5294.
207. H. F. Stanley and P. Meakin, Multifractal phenomena in physics and chemistry, Nature, 335(1988), 405-409.
208. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, Fractal measures and their singularities, Phys. Rev. A, 33(1986), 1141.
209. B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, New York, 1983.
210. E. Klein, R. Mislovaty, I. Kanter, and W. Kinzel, Public-channel cryptography using chaos synchronization, Phys. Rev. E, 72-1(2005), article 016214, part 2.
211. X. H. Zhang and S. B. Zhou, Chaos synchronization for bi-directional coupled two-neuron systems with discrete delays, in J. Wang, X. Liao, and Z. Yi, eds., Advances in Neural Networks: ISNN 2005 (2nd International Symposium on Neural Networks, Chongqing, China, May 30-June 1, 2005) Proceedings, Part I, Lecture Notes in Computer Science, Vol. 3496, Springer-Verlag, New York, 2005, 351-356.
212. Y. N. Li, L. Chen, Z. S. Cai, and X. Z. Zhao, Experimental study ofchaos synchronization in the Belousov-Zhabotinsky chemical system, Chaos Solitons Fractals, 22-4(2004), 767-771.
213. S. H. Strogatz, Sync: The Emerging Science of Spontaneous Order, Theia, New York, 2003.
214. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, The synchronization of chaotic systems, Phys. Rep., 366(2002), 1-101
215. E. Mosekilde, Y. Maistrenko, and D. Postnov, Chaotic Synchronization, World Scientific, Singapore, 2002.
216. C. W. Wu, Synchronization in Coupled Chaotic Circuits and Systems, World Scientific, Singapore, 2002.
217. L. Glass, Synchronization and rhythmic processes in physiology, Nature, 410(2001), 277-284.
218. T. Kapitaniak, Chaos for Engineers: Theory, Applications and Control, 2nd ed., Springer-Verlag, New York, 2000.
219. S. Yousefi, Y. Maistrenko, and S. Popovych, Complex dynamics in a simple model of interdependent open economies, Discrete Dynam. Nature Society, 5-3(2000), 161-177.
220. S. Lynch and A. L. Steele, Controlling chaos in nonlinear bistable optical resonators, Chaos Solitons Fractals, 11-5(2000), 721-728.
221. M. Buchanan, Fascinating rhythm, New Scientist, 3 January (1998), 20-25.
222. L. Luo and P. L. Chu, Optical secure communications with chaotic erbiumdoped fiber lasers, J. Optical Soc. Amer. B, 15(1998), 2524-2530.
223. N. P. Chau, Controlling chaos by periodic proportional pulses, Phys. Lett. A, 234(1997), 193-197.
224. H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Generalized synchronization of chaos: The auxiliary system approach, Phys. Rev. E, 53-5(1996), 4528-4535.
225. T. Kapitaniak, Controlling Chaos: Theoretical and Practical Methods in Non-Linear Dynamics, Academic Press, New York, 1996.
226. K. M. Cuomo and A. V. Oppenheim, Circuit implementationof synchronized chaos with applications to communications, Phys. Rev. Lett., 71(1993), 65-68.
227. A. Garfinkel, M. L. Spano, W. L. Ditto, and J. N. Weiss, Controlling cardiac chaos, Science, 257(1992), 1230-1235.
228. R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system, Phys. Rev. Lett., 68(1992), 1259-1262.
229. E. R. Hunt, Stabilizing high-period orbits in a chaotic system: The diode resonator, Phys. Rev. Lett., 67(1991), 1953-1955.
230. J. Singer, Y.-Z. Wang, and H. H. Bau, Controlling a chaotic system, Phys. Rev. Lett., 66(1991), 1123-1125.
231. W. L. Ditto, S. N. Rausseo, and M. L. Spano, Experimental control of chaos, Phys. Rev. Lett., 65(1990), 3211-3214.
232. T. Shinbrot, C. Grebogi, E. Ott, and J. A. Yorke, Using chaos to direct trajectories to targets, Phys. Rev. Lett., 65(1990), 3215-3218.
233. L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., 64(1990), 821-824.
234. E. Ott, C. Grebogi, and J. A. Yorke, Controlling chaos, Phys. Rev. Lett., 64(1990), 1196-1199.
235. E. M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, Computational Neuroscience, MIT Press, Cambridge, MA, 2006.
236. S. Samarasinghe, Neural Networks for Applied Sciences and Engineering, Auerbach, Boca Raton, FL, 2006.
237. J. A. Rothwell, The word liar, New Scientist, March (2003), 51.
238. Z. G. Bandar, D. A. McLean, J. D. O'Shea, and J. A. Rothwell, Analysis of the Behaviour of a Subject, International Publication Number WO 02/087443 A1, 2002.
239. M. Di Marco, M. Forti and A. Tesi, Existence and characterization of limit cycles in nearly symmetric neural networks, IEEE Trans. Circuits Ssystems 1 Fund. Theory Appl., 49(2002), 979-992.
240. P. Dayan and L. F. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, MIT Press, Cambridge, MA, 2001.
241. I. W. Sandberg, ed., J. T. Lo, C. L. Fancourt, J. Principe, S. Haykin, and S. Katargi, Nonlinear Dynamical Systems: Feedforward Neural Network Perspectives, Adaptive Learning Systems to Signal Processing, Communications, and Control, Wiley-Interscience, New York, 2001.
242. W. J. Freeman, Neurodynamics: An Exploration in Mesoscopic Brain Dynamics, Perspectives in Neural Computing, Springer-Verlag, New York, 2000.
243. B. Kosko, Neural networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence, Prentice-Hall, Upper Saddle River, NJ, 1999.
244. J. V. Sanchez-Andrés, eds., Foundations and Tools for Neural Modeling: International Work-Conference on Artificial and Natural Neural Networks (IWANN'99, Alicante, Spain, June 2-4, 1999) Proceedings, Vol. I, Lecture Notes in Computer Science, Vol. 1606, Springer-Verlag, Berlin, 1999, 377-384.
245. S. S. Haykin, Neural Networks: A Comprehensive Foundation, 2nd ed., Prentice-Hall, Upper Saddle River, NJ, 1998.
246. F. Pasemann, A simple chaotic neuron, Phys. D, 104(1997), 205-211.
247. M. T. Hagan, H. B. Demuth, and M. H. Beale, Neural Network Design, Brooks-Cole, Pacific Grove, CA, 1995.
248. S. J. Schiff, K. Jerger, D. H. Doung, T. Chang, M. L. Spano, and W. L. Ditto, Controlling chaos in the brain, Nature, 370(1994), 615.
249. D. E. Rumelhart and J. L. McClelland, eds., Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. 1, MIT Press, Cambridge, MA, 1986.
250. J. J. Hopfield and D. W. Tank, Neural computation of decisions in optimization problems, Biol. Cybernet., 52(1985), 141-154.
251. J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Nat. Acad. Sci., 81(1984), 3088-3092.
252. J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci., 79(1982), 2554-2558;
253. reprinted in J. A. Anderson and E. Rosenfeld, eds, Neurocomputing: Foundations of Research, MIT Press, Cambridge, MA, 1988, 448-453.
254. T. Kohonen, Self-organized formation of topologically correct feature maps, Biol. Cybernet., 43(1982), 59-69;
255. reprinted in J. A. Anderson and E. Rosenfeld, eds, Neurocomputing: Foundations of Research, MIT Press, Cambridge, MA, 1988, 554-568.
256. M. Minsky and S. Papert, Perceptrons, MIT Press, Cambridge, MA, 1969.
257. B. Widrow and M. E. Hoff, Adaptive switching circuits, in 1960 IRE WESCON Convention Record, Part 4, IRE, New York, 1960, 96-104.
258. F. Rosenblatt, The perceptron: Aprobabalistic model for information storage and organization in the brain, Psychological Rev., 65(1958), 386-408.
259. D. O. Hebb, The Organization of Behaviour, Wiley, New York, 1949.
260. W. McCulloch and W. Pitts, A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophys., 5(1943), 115-133.
261. S. S. Abdullaev, Construction of Mappings for Hamiltonian Systems and Their Applications, Lecture Notes in Physics, Springer-Verlag, New York, 2006.
262. M. L. Abell and J. P. Braselton, Differential Equations with Mathematica, 3rd ed., Academic Press, New York, 2004.
263. P. S. Addison, Fractals and Chaos: An Illustrated Course, Institute of Physics, Bristol, PA, 1997.
264. G. P. Agrawal, Applications in Nonlinear Fiber Optics, Academic Press, New York, London, 2001.
265. G. P. Agrawal, Nonlinear Fibre Optics, 3rd ed., Academic Press, New York, London, 2001.
266. H. Anton and C. Rorres, Elementary Linear Algebra, Wiley, New York, 2005.
267. N. Arnold, Chemical Chaos, Hippo, London, 1997.
268. D. K. Arrowsmith and C. M. Place, An Introduction to Dynamical Systems, Cambridge University Press, Cambridge, UK, 1990.
269. D. K. Arrowsmith and C. M. Place, Dynamical Systems, Chapman and Hall, London, 1992
270. A. Bacciotti and L. Rosier, Liapunov Functions and Stability in Control Theory, Springer-Verlag, New York, 2001.
271. S. Barnet, Discrete Mathematics, Addison-Wesley, Reading, MA, 1998.
272. G. Baumann, Mathematica for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics, Springer-Verlag, New York, 2005.
273. G. Baumann, Mathematica for Theoretical Physics: Electrodynamics, Quantum Mechanics, General Relativity, and Fractals, Springer-Verlag, New York, 2005.
274. B. Bhattacharya and M. Majumdar, Random Dynamical Systems: Theory and Applications, Cambridge University Press, Cambridge, UK, 2007.
275. A. V. Bolsinov and A. T. Fomenko, Integrable Hamiltonian Systems: Geometry, Topology, Classification, CRC Press, Boca Raton, FL, 2004.
276. F. Brauer nd C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, New York, 2001.
277. H. Broer, I. Hoveijn, G. Lunter, and G. Vegter, Bifurcations in Hamiltonian Systems: Computing Singularities by Gröbner Bases, Lecture Notes in Mathematics, Springer-Verlag, New York, 2003.
278. R. Bronson and G. Costa, Schaum's Outline of Differential Equations, 3rd ed., McGraw-Hill, New York, 2006.
279. B. Buchberger, ed., Gröbner Bases and Applications, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, UK, 1998.
280. B. Buchberger, On Finding a Vector Space Basis of the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal, Ph. D. thesis, University of Innsbruck, Innsbruck, Austria, 1965 (in German).
281. J. Chiasson and J. J. Loiseau, Applications of Time Delay Systems, Springer-Verlag, New York, 2007.
282. C-ODE-E (Consortium for ODE Experiments), ODEArchitect: The Ultimate ODE Power Tool, Wiley, New York, 1999.
283. J. Cronin, Differential Equations: Introduction and Qualitative Theory, 2nd ed., Marcel Dekker, New York, 1994.
284. R. M. Crownover, Introduction to Fractals and Chaos, Jones and Bartlett, Sudbury, MA, 1995.
285. P. Dayan and L. F. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, MIT Press, Cambridge, MA, 2001
286. W. R. Derrick and S. I. Grossman, Elementary Differential Equations, 4th ed., Addison-Wesley, Reading, MA, 1997.
287. M. Demazure and D. Chillingworth (translator), Bifurcations and Catastrophes: Chemistry and Engineering, Springer-Verlag, New York, 2001.
288. R. L. Devaney and L. Keen, eds., Complex Dynamics: Twenty-Five Years After the Appearance of the Mandelbrot Set, Contemporary Mathematics, American Mathematical Society, Providence, RI, 2005.
289. R. L. Devaney, M. Hirsch, and S. Smale, Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2nd ed., Academic Press, New York, 2003.
290. R. L. Devaney, The Mandelbrot Set and Julia Sets: A Tool kit of Dynamics Activities, Key Curriculum Press, Emeryville, CA, 2002.
291. E. Don, Schaum's Outline of Mathematica, McGraw-Hill, New York, 2000.
292. K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Wiley, New York, 2003.
293. R. Field and M. Burger, eds., Oscillations and Travelling Waves in Chemical Systems, Wiley, New York, 1985.
294. G. W. Flake, The Computational Beauty of Nature: Computer Explorations of Fractals, MIT Press, Cambridge, MA, 1998.
295. W. J. Freeman, Neurodynamics: An Exploration in Mesoscopic Brain Dynamics, Perspectives in Neural Computing, Springer-Verlag, New York, 2000.
296. H. M. Gibbs, Optical Bistability: Controlling Light with Light, Academic Press, New York, London, 1985.
297. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 3rd ed., Springer-Verlag, New York, 1990.
298. M. T. Hagan, H. B. Demuth, and M. H. Beale, Neural Network Design, Brooks-Cole, Pacific Grove, CA, 1995.
299. J. K. Hale, L. T. Magalhaes, and W. Oliva, Dynamics in Infinite Dimensions, 2nd ed., Springer-Verlag, New York, 2002.
300. D. Harte, Multifractals: Theory and Applications, Chapman and Hall, London, 2001.
301. P. Hartman, Ordinary Differential Equations, Wiley, New York, 1964.
302. A. Hastings, Population Biology: Concepts and Models, Springer-Verlag, New York, 2005.
303. S. S. Haykin, Neural Networks: A Comprehensive Foundation, 2nd ed., Prentice-Hall, Upper Saddle River, NJ, 1998.
304. D. O. Hebb, The Organization of Behaviour, Wiley, New York, 1949.
305. R. C. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, 2nd ed., Oxford University Press, Oxford, UK, 2000.
306. E. J. Hinch, Perturbation Methods, Cambridge University Press, Cambridge, UK, 2002.
307. M. W. Hirsch and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, New York, 1974.
308. R. A. Holmgrem, A First Course in Discrete Dynamical Systems, Springer-Verlag, Berlin, New York, Heidelberg, 1996.
309. K. Ikeda and M. Murota, Imperfect Bifurcations in Structures and Materials, Springer-Verlag, New York, 2002.
310. Yu. S. Il'yashenko, Finiteness Theorems for Limit Cycles, Translations of Mathematical Monographs, Vol. 94, American Mathematical Society, Providence, RI, 1991.
311. G. Iooss and D. D. Joseph, Elementary Stability and Bifurcation Theory, Springer-Verlag, Berlin, New York, Heidelberg, 1997.
312. E. M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, Computational Neuroscience, MIT Press, Cambridge, MA, 2006.
313. D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, 3rd ed., Oxford University Press, Oxford, UK, 1999.
314. T. Kapitaniak, Controlling Chaos: Theoretical and Practical Methods in Non-Linear Dynamics, Academic Press, New York, 1996.
315. T. Kapitaniak, Chaos for Engineers: Theory, Applications and Control, 2nd ed., Springer-Verlag, New York, 2000.
316. D. Kaplan and L. Glass, Understanding Nonlinear Dynamics, Springer-Verlag, Berlin, New York, Heidelberg, 1995.
317. W. Kelley and A. Peterson, The Theory of Differential Equations: Classical and Qualitative, Prentice-Hall, Upper Saddle River, NJ, 2003.
318. A. C. King, J. Billingham, and S. R. Otto, Differential Equations: Linear, Nonlinear, Ordinary, Partial, Cambridge University Press, Cambridge, UK, 2003.
319. B. Kosko, Neural networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence, Prentice-Hall, Upper Saddle River, NJ, 1999.
320. E. J. Kostelich and D. Armbruster, Introductory Differential Equations, Addison-Wesley, Reading, MA, 1997.
321. S. G. Krantz, Differential Equations Demystified, McGraw-Hill, New York, 2004.
322. M. R. S. Kulenovic and O. Merino, Discrete Dynamical Systems and Differential Equations with Mathematica, Chapman and Hall, London, 2002.
323. J. P. Lasalle, Stability by Liapunov's Direct Method: With Applications, Academic Press, New York, 1961.
324. N. Lauritzen, Concrete Abstract Algebra: From Numbers to Gröbner Bases, Cambridge University Press, Cambridge, UK, 2003.
325. H. A. Lauwerier, Fractals: Images of Chaos, Penguin, New York, 1991.
326. J. H. Liu, A First Course in the Qualitative Theory of Differential Equations, Prentice-Hall, Upper Saddle River, NJ, 2002.
327. A. J. Lotka, Elements of Physical Biology, William and Wilkins, Baltimore, 1925.
328. S. Lynch, Dynmical Systems with Applications Using Maple, Birkhaüser Boston, Cambridge, MA, 2001.
329. R. N. Madan, Chua's Circuit: A Paradigm for Chaos, World Scientific, Singapore, 1993.
330. P. Mandel, Theoretical Problems in Cavity Nonlinear Optics, Cambridge University Press, Cambridge, UK, 2005.
331. B. B. Mandelbrot and R. L. Hudson, The (Mis) Behavior of Markets: A Fractal View of Risk, Ruin And Reward, Perseus Books, New York, 2006.
332. B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, New York, 1983.
333. R. M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton, NJ, 1974.
334. D. McMahon and D. M. Topa, A Beginner's Guide to Mathematica, Chapman and Hall, London, CA, 2006.
335. M. Minsky and S. Papert, Perceptrons, MIT Press, Cambridge, MA, 1969.
336. E. Mosekilde, Y. Maistrenko, and D. Postnov, Chaotic Synchronization, World Scientific, Singapore, 2002
337. J. Murdock, Normal Forms and Unfoldings for Local Dynamical Systems, Springer-Verlag, New York, 2003.
338. H. Nagashima and Y. Baba, Introduction to Chaos: Physics and Mathematics of Chaotic Phenomena, Institute of Physics, Bristol, PA, 1999.
339. A. H. Nayfeh, Perturbation Methods, Wiley-Interscience, New York, 2000.
340. A. H. Nayfeh, Method of Normal Forms, Wiley Series in Nonlinear Science, Wiley, New York, 1993.
341. V. V. Nemitskii and V. V. Stepanov, Qualitative Theory of Differential Equations, Princeton University Press, Princeton, NJ, 1960.
342. H.-O. Peitgen, H. Jürgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer-Verlag, New York, 1992.
343. H.-O. Peitgen, H. Jürgens, D. Saupe, and C. Zahlten, Fractals: An Animated Discussion, Spektrum Akademischer Verlag, Heidelberg, 1989;
344. W. H. Freeman, New York, 1990.
345. H.-O. Peitgen, ed., E. M. Maletsky, H. Jürgens, T. Perciante, D. Saupe, and L. Yunker, Fractals for the Classroom: Strategic Activities, Vol. 1, Springer-Verlag, New York, 1991.
346. H.-O. Peitgen, ed., E. M. Maletsky, H. Jürgens, T. Perciante, D. Saupe, and L. Yunker, Fractals for the Classroom: Strategic Activities, Vol. 2, Springer-Verlag, New York, 1993.
347. H.-O. Peitgen and P. H. Richter, The Beauty of Fractals, Springer-Verlag, Berlin, New York, Heidelberg, 1986.
348. L. Perko, Differential Equations and Dynamical Systems, 3rd ed., Springer-Verlag, Berlin, New York, Heidelberg, 2006.
349. Ye Yan Qian, Theory of Limit Cycles, Translations of Mathematical Monographs, Vol. 66, American Mathematical Society, Providence, RI, 1986.
350. B. Rai and D. P. Choudhury, Elementary Ordinary Differential Equations, Alpha Science International, Oxford, UK, 2005.
351. J. Rayleigh, The Theory of Sound, Dover, New York, 1945.
352. D. Richards, Advanced Mathematical Methods with Mathematica, Cambridge University Press, Cambridge, UK, 2001.
353. J. C. Robinson, An Introduction to Ordinary Differential Equations, Cambridge University Press, Cambridge, UK, 2004
354. C. Rocsoreanu, A. Georgeson, and N. Giurgiteanu, The Fitzhugh-Nagumo Model: Bifurcation and Dynamics, Kluwer, Dordrecht, Netherlands, 2000.
355. C. C. Ross, Differential Equations: An Introduction with Mathematica, Springer-Verlag, New York, 2004.
356. D. E. Rumelhart and J. L. McClelland, eds., Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. 1, MIT Press, Cambridge, MA, 1986.
357. S. Samarasinghe, Neural Networks for Applied Sciences and Engineering, Auerbach, Boca Raton, FL, 2006.
358. T. Schneider, Nonlinear Optics in Telecommunications, Springer-Verlag, New York, 2004.
359. S. K. Scott, Oscillations, Waves, and Chaos in Chemical Kinetics, Oxford Science Publications, Oxford, UK, 1994.
360. R. Seydel, Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos, Springer-Verlag, Berlin, New York, Heidelberg, 1994.
361. B. Shivamoggi, Perturbation Methods for Differential Equations, Birkhäuser Boston, Cambridge, MA, 2006.
362. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, Springer-Verlag, New York, 1982.
363. M. R. Spiegel, Schaum's Outline of Laplace Transforms, McGraw-Hill, New York, 1965.
364. S. H. Strogatz, Sync: The Emerging Science of Spontaneous Order, Theia, New York, 2003.
365. S. H. Strogatz, Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering, Perseus Books, New York, 2001.
366. H. R. Thieme, Mathematics in Population Biology, Princeton Series in Theoretical and Computational Biology, Princeton University Press, Princeton, NJ, 2003.
367. J. M. T. Thompson and H. B. Stewart, Nonlinear Dynamics and Chaos, 2nd ed., Wiley, New York, 2002.
368. M. Trott, The Mathematica Guidebook for Numerics, Springer-Verlag, New York, 2005.
369. M. Trott, The Mathematica Guidebook for Symbolics, Springer-Verlag, New York, 2005
370. M. Trott, The Mathematica Guidebook: Graphics, Springer-Verlag, New York, 2004.
371. M. Trott, The Mathematica Guidebook: Programming, Springer-Verlag, NewYork, 2004.
372. G. Turrell, Mathematics for Chemistry and Physics, Academic Press, New York, 2001.
373. V. Volterra, Theory of Functionals and of Integral and Integro-Differential Equations, Dover, New York, 2005.
374. D. M. Wang and Z. Zheng, eds., Differential Equations with Symbolic Computation, Birkhäuser, Basel, Cambridge, MA, 2005.
375. D. M. Wang, Elimination Practice: Software Tools and Applications, Imperial College Press, London, 2004.
376. B. West, S. Strogatz, J. M. McDill, J. Cantwell, and H. Hohn, Interactive Differential Equations, Version 2.0, Addison-Wesley, Reading, MA, 1997.
377. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, Berlin, New York, Heidelberg, 1990.
378. R. Williams, Introduction to Differential Equations and Dynamical Systems, McGraw-Hill, New York, 1997.
379. S. Wolfram, The Mathematica Book, 6th ed. (electronic), Wolfram Media, Champaign, IL, 2007; included with Mathematica® Version 6.0.
380. C. W. Wu, Synchronization in Coupled Chaotic Circuits and Systems, World Scientific, Singapore, 2002.
381. J. A. Yorke, contributor, K. Alligood, ed., and T. Sauer, ed., Chaos: An Introduction to Dynamical Systems, Springer-Verlag, New York, 1996.
382. G. M. Zaslavsky, Physics of Chaos in Hamiltonian Systems, World Scientific, Singapore, 1998.
383. Zhang Zhifen, Ding Tongren, Huang Wenzao, and Dong Zhenxi, Qualitative Theory of Differential Equations, Translation of Mathematical Monographs, Vol. 102, American Mathematical Society, Providence, RI, 1992.
384. D. G. Zill, A First Course in Differential Equations with Modeling Applications, Brooks-Cole, Belmont, CA, 2000
385. H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Generalized synchronization of chaos: The auxiliary system approach, Phys. Rev. E, 53-5(1996), 4528-4535.
386. A. Agarwal and N. Ananthkrishnan, Bifurcation analysis for onset and cessation of surge in axial flow compressors, Internat. J. Turbo Jet Engines, 17-3(2000), 207-217.
387. E. Ahmed, A. El-Misiery, and H. N. Agiza, On controlling chaos in an inflation-unemployment dynamical system, Chaos Solitons Fractals, 10-9(1999), 1567-1570.
388. M. Alber and J. Peinke, Improved multifractal box-counting algorithm, virtual phase transitions, and negative dimensions, Phys. Rev. E, 57-5(1998), 5489-5493.
389. Z. G. Bandar, D. A. McLean, J. D. O'Shea, and J. A. Rothwell, Analysis of the Behaviour of a Subject, International Publication Number WO 02/087443 A1, 2002.
390. N. Bautin, On the number of limit cycles which appear with the variation of the coefficients from an equilibrium point of focus or centre type, Amer. Math. Soc. Trans., 5(1962), 396-414.
391. T. Bischofberger and Y. R. Shen, Theoretical and experimental studyofthe dynamic behaviour of a nonlinear Fabry-Perot interferometer, Phys. Rev. A, 19(1979), 1169-1176.
392. S. Blacher, F. Brouers, R. Fayt, and P. Teyssié, Multifractal analysis: A new method for the characterization of the morphology of multicomponent polymer systems, J. Polymer Sci. B, 31(1993), 655-662.
393. T. R. Blows and N. G. Lloyd, The numberofsmall-amplitude limit cycles of Liénard equations, Math. Proc. Cambridge Philos. Soc., 95(1984), 359-366.
394. T. R. Blows and L. M. Perko, Bifurcation of limit cycles from centres and separatrix cycles of planar analytic systems, SIAM Rev., 36(1994), 341-376.
395. T. R. Blows and C. Rousseau, Bifurcation at infinity in polynomial vector fields, J. Differential Equations, 104(1993), 215-242.
396. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, The synchronization of chaotic systems, Phys. Rep., 366(2002), 1-101.
397. J. Borresen and S. Lynch, Further investigation of hysteresis in Chua's circuit, Internat. J. Bifurcation Chaos, 12(2002), 129-134
398. A. D. Bruno and V. F. Edneral, Normal forms and integrability of ODE systems, in Computer Algebra in Scientific Computing: Proceedings, Lecture Notes in Computer Science, Vol. 3718, Springer-Verlag, New York, 2005, 65-74.
399. M. Buchanan, Fascinating rhythm, New Scientist, 3 January (1998), 20-25.
400. E. Chambon-Dubreuil, P. Auger, J. M. Gaillard, and M. Khaladi, Effect of aggressive behaviour on age-structured population dynamics, Ecological Model, 193(2006), 777-786.
401. N. P. Chau, Controlling chaos by periodic proportional pulses, Phys. Lett. A, 234(1997), 193-197.
402. E. S. Cheb-Terrab and H. P. De Oliveira, Poincaré sections of Hamiltonian systems, Comput. Phys. Comm., 95(1996), 171.
403. L. A. Cherkas, Conditions for a Liénard equation to have a centre, Differentsial'nye Uravneniya, 12(1976), 201-206.
404. A. B. Chhabra, C. Meneveau, R. V. Jensen, and K. R. Sreenivasan, Direct determination of the f (a) singularity spectrum and its application to fully developed turbulence, Phys. Rev. A, 40-9(1989), 5284-5294.
405. C. J. Christopher and N. G. Lloyd, Polynomial systems: A lower bound for the Hilbert numbers, Proc. Roy. Soc. London Ser. A, 450(1995), 219-224.
406. C. J. Christopher and N. G. Lloyd, Small-amplitude limit cycles in polynomial Liénard systems, Nonlinear Differential Equations Appl, 3(1996), 183-190.
407. C. J. Christopher and S. Lynch, Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces, Nonlinearity, 12(1999), 1099-1112.
408. W. A. Coppel, Some quadratic systems with at most one limit cycle, in U. Kirchgraber and H. O. Walther, eds., Dynamics Reported, Vol. 2, Wiley/Teubner, New York, Stuttgart, 1988, 61-68.
409. K. M. Cuomo and A. V. Oppenheim, Circuit implementation of synchronized chaos with applications to communications, Phys. Rev. Lett., 71(1993), 65-68.
410. R. H. Day, Irregular growth cycles, Amer. Econ. Rev., 72(1982), 406-414.
411. M. Di Marco, M. Forti and A. Tesi, Existence and characterization of limit cycles in nearly symmetric neural networks, IEEE Trans. Circuits Ssystems 1 Fund. Theory Appl, 49(2002), 979-992.
412. W. L. Ditto, S. N. Rausseo, and M. L. Spano, Experimental control of chaos, Phys. Rev. Lett., 65(1990), 3211-3214.
413. N. J. Doran and D. Wood, Nonlinear-optical loop mirror, Optics Lett., 13(1988), 56-58.
414. F. Dumortier, D. Panazzolo, and R. Roussarie, More limit cycles than expected in Liénard equations, Proc. Amer. Math. Soc., 135-6(2007), 1895-1904.
415. F. Dumortier and L. Chengzhi, On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations, Nonlinearity, 9(1996), 1489-1500.
416. F. Dumortier and L. Chengzhi, Quadratic Liénard equations with quadratic damping, J. Differential Equations, 139(1997), 41-59.
417. J. Ecalle, J. Martinet, J. Moussu, and J. P. Ramis, Non-accumulation des cycleslimites I, C. R. Acad. Sci. Paris Sér. I Math., 304(1987), 375-377.
418. J. P. Eckmann, S. O. Kamphorst, D. Ruelle, and S. Ciliberto, Liapunov exponents from time series, Phys. Rev. A, 34-6(1986), 4971-4979.
419. S. Ellner and P. Turchin, Chaos in a noisy world: New methods and evidence from time-series analysis, Amer. Naturalist, 145-3(1995), 343-375.
420. K. J. Falconer and B. Lammering, Fractal properties of generalized Sierpiński triangles, Fractals, 6-1(1998), 31-41.
421. F. S. Felber and J. H. Marburger, Theory of nonresonant multistable optical devices, Appl. Phys. Lett., 28(1976), 731.
422. W. J. Firth, Stability of nonlinear Fabry-Perot resonators, Optics Comm., 39-5(1981), 343-346.
423. R. Fitzhugh, Impulses and physiological states in theoretical models of nerve membranes, J. Biophys., 1182(1961), 445-466.
424. A. Garfinkel, M. L. Spano, W. L. Ditto, and J. N. Weiss, Controlling cardiac chaos, Science, 257(1992), 1230-1235.
425. K. Geist, U. Parlitz, and W. Lauterborn, Comparison of different methods for computing Lyapunov exponents, Progr. Theoret. Phys., 83(1990), 875-893.
426. H. Giacomini and S. Neukirch, Improving a method for the study of limit cycles of the Liénard equation, Phys. Rev. E, 57(1998), 6573-6576.
427. L. Glass, Synchronization and rhythmic processes in physiology, Nature, 410(2001), 277-284.
428. G. A. Gottwald and I. Melbourne, A new test for chaos in deterministic systems, Proc. Roy. Soc. London A, 460-2042(2004), 603-611
429. S. R. Hall, M. A. Duffy, and C. E. Cáceres, Selective predation and productivity jointly drive complex behavior in host-parasite systems, Amer. Naturalist, 165-1(2005), 70-81.
430. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, Fractal measures and their singularities, Phys. Rev. A, 33(1986), 1141.
431. S. M. Hammel, C. K. R. T. Jones, and J. V. Moloney, Global dynamical behavior of the optical field in a ring cavity, J. Optical Soc. Amer. B, 2-4(1985), 552-564.
432. M. Hénon, Numerical study of quadratic area-preserving mappings, Quart. Appl. Math., 27(1969), 291-311.
433. A. L. Hodgkin and A. F. Huxley, A qualitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol., 117(1952), 500-544;
434. reproduced in Bull. Math. Biol., 52(1990), 25-71.
435. J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci., 79(1982), 2554-2558;
436. reprinted in J. A. Anderson and E. Rosenfeld, eds, Neurocomputing: Foundations of Research, MIT Press, Cambridge, MA, 1988, 448-453.
437. J. J. Hopfield and D. W. Tank, Neural computation of decisions in optimization problems, Biol. Cybernet., 52(1985), 141-154.
438. J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Nat. Acad. Sci., 81(1984), 3088-3092.
439. S. B. Hsu and T. W. Hwang, Hopf bifurcation analysis for a predator-prey system of Holling and Leslie type, Taiwan J. Math., 3(1999), 35-53.
440. Li Hua, D. Ze-jun, and Wu Ziqin, Multifractal analysis of the spatial distribution of secondary-electron emission sites, Phys. Rev. B, 53-24(1996), 16631-16636.
441. E. R. Hunt, Stabilizing high-period orbits in a chaotic system: The diode resonator, Phys. Rev. Lett., 67(1991), 1953-1955.
442. Y. Il'yashenko, Centennial history of Hilbert's 16th problem, Bull. Amer. Math. Soc., 39(2002), 301-354.
443. K. Ikeda, H. Daido, and O. Akimoto, Optical turbulence: Chaotic behaviour of transmitted light from a ring cavity, Phys. Rev. Lett., 45-9(1980), 709-712.
444. Y. H. Ja, Multiple bistability in an optical-fibre double-ring resonator utilizing the Kerr effect, IEEE J. Quantum Electron., 30-2(1994), 329-333.
445. S. Jal and T. G. Hallam, Effects of delay, truncations and density dependence in reproduction schedules on stability of nonlinear Leslie matrix models, J. Math. Biol., 31-4(1993), 367-395
446. J. Jiang, H. Maoan, Y. Pei, and S. Lynch, Limit cycles in two types of symmetric Liénard systems, Internat. J. Bifurcation Chaos, 17-6(2007), 2169-2174.
447. Li Jibin and Li Chunfu, Global bifurcationof planar disturbed Hamiltonian systems and distributions of limit cycles of cubic systems, Acta Math. Sinica, 28(1985), 509-521.
448. E. Klein, R. Mislovaty, I. Kanter, and W. Kinzel, Public-channel cryptography using chaos synchronization, Phys. Rev. E, 72-1(2005), article 016214, part 2.
449. T. Kohonen, Self-organized formation of topologically correct feature maps, Biol. Cybernet., 43(1982), 59-69;
450. reprinted in J. A. Anderson and E. Rosenfeld, eds, Neurocomputing: Foundations of Research, MIT Press, Cambridge, MA, 1988, 554-568.
451. B. Krauskopf, H. M. Osinga, E. J. Doedel, M. E. Henderson, J. M. Guckenheimer, A. Vladimirsky, M. Dellnitz, and O. Junge, A survey of methods for computing (un) stable manifolds of vector fields, Internat. J. Bifurcation Chaos, 15-3(2005), 763-791.
452. A. Lasota, Ergodic problems in biology, in Dynamical Systems, Vol. 2: Warsaw, Astérisque, Vol. 50, Société Mathématique de France, Paris, 1977, 239-250.
453. Y. Lenbury S. Rattanamongkonkul, N. Tumrasvin, and S. Amornsamankul, Predator-prey interaction coupled by parasitic infection: Limit cycles and chaotic behaviour, Math. Comput. Model., 30-9-10(1999), 131-146.
454. Y. N. Li, L. Chen, Z. S. Cai, and X. Z. Zhao, Experimental study of chaos synchronization in the Belousov-Zhabotinsky chemical system, Chaos Solitons Fractals, 22-4(2004), 767-771.
455. H. Li and K. Ogusu, Analysis of optical instability in a double-coupler nonlinear fibre ring resonator, Optics Comm., 157(1998), 27-32.
456. J. Li, Hilbert's sixteenth problem and bifurcations of planar polynomial vector fields, Internat. J. Bifurcation Chaos, 13(2003), 47-106.
457. T. Y. Li and J. A. Yorke, Period three implies chaos, Amer. Math. Monthly, 82(1975), 985-992.
458. A. Liénard, Étude des oscillations entrenues, Rev. Gén. Électricité, 23(1928), 946-954.
459. A. Lins, W. De Melo, and C. Pugh, On Liénards equation with linear damping, in J. Palis and M. do Carno, eds., Geometry and Topology, Lecture Notes in Mathematics, Vol. 597, Springer-Verlag, Berlin, 1977, 335-357
460. N. G. Lloyd, Limit cycles of polynomial systems, in T. Bedford and J. Swift, eds., New Directions in Dynamical Systems, London Mathematical Society Lecture Notes Series, Vol. 127, Cambridge University Press, Cambridge, UK, 1988.
461. N. G. Lloyd and S. Lynch, Small-amplitude limit cycles of certain Liénard systems, Proc. Roy. Soc. London Ser. A, 418(1988), 199-208.
462. V. N. Lopatin and S. V. Rosolovsky, Evaluation of the state and productivity of moose populations using Leslie matrix analyses, Alces, Suppl. 2(2002), 77-80.
463. E. N. Lorenz, Deterministic non-periodic flow, J. Atmos. Sci., 20(1963), 130-141.
464. L. Luo and P. L. Chu, Optical secure communications with chaotic erbium-doped fiber lasers, J. Optical Soc. Amer. B, 15(1998), 2524-2530.
465. S. Lynch, Analysisof a blood cell population model, Internat. J. Bifurcation Chaos, 15(2005), 2311-2316.
466. S. Lynch and Z. G. Bandar, Bistable neuromodules, Nonlinear Anal. Theory Methods Appl., 63(2005), 669-677.
467. S. Lynch and A. L. Steele, Controlling chaosinnonlinear bistable optical resonators, Chaos Solitons Fractals, 11-5(2000), 721-728.
468. S. Lynch and C. J. Christopher, Limit cycles in highly nonlinear differential equations, J. Sound Vibration, 224-3(1999), 505-517.
469. S. Lynch, A. L. Steele, and J. E. Hoad, Stability analysis of nonlinear optical resonators, Chaos Solitons Fractals, 9-6(1998), 935-946.
470. J. Mach, F. Mas, and F. Sagués, Two representations in multifractal analysis, J. Phys. A, 28(1995), 5607-5622.
471. A. Marasco and C. Tenneriello, Periodic solutions of a 2D-autonomous system using Mathematica, Math. Comput. Model., 45-5-6(2007), 681-693.
472. J. H. Marburger and F. S. Felber, Theory of a lossless nonlinear Fabry-Perot interferometer, Phys. Rev. A, 17(1978), 335-342.
473. R. Matthews, Catch the wave, New Scientist, 162-2189(1999), 27-32.
474. W. McCulloch and W. Pitts, A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophys., 5(1943), 115-133.
475. S. L. Mills, G. C. Lees, C. M. Liauw, R. N. Rothon and S. Lynch, Prediction ofphysical properties following the dispersion assessment of flame retardant filler/polymer composites based on the multifractal analysis of SEM images, J. Macromolecular Sci. B Phys., 44-6(2005), 1137-1151
476. S. L. Mills, G. C. Lees, C. M. Liauw, and S. Lynch, An improved method for the dispersion assessment of flame retardent filler/polymer systems based on the multifractal analysis of SEM images, Macromolecular Materials Engrg., 289-10(2004), 864-871.
477. H. N. Moreira, Liénard-type equations and the epidemiologyofmaleria, Ecological Model., 60(1992), 139-150.
478. J. Moser, Recent developments in the theory of Hamiltonian systems, SIAM Rev., 28-4(1986), 459-485.
479. J. Muller, O. K. Huseby, and A. Saucier, Influence of multifractal scaling of pore geometry on permeabilities of sedimentary rocks, Chaos Solitons Fractals, 5-8(1995), 1485-1492.
480. J. Nagumo, S. Arimoto, and S. Yoshizawa, An active pulse transmission line simulating 1214-nerve axons, Proc. IRL, 50(1970), 2061-2070.
481. H. Natsuka, S. Asaka, H. Itoh, K. Ikeda, and M. Matouka, Observation of bifurcation to chaos in an all-optical bistable system, Phys. Rev. Lett., 50(1983), 109-112.
482. K. Ogusu, A. L. Steele, J. E. Hoad, and S. Lynch, Corrections to and comments on "Dynamic behaviour of reflection optical bistability in a nonlinear fibre ring resonator", IEEE J. Quantum Electron., 33(1997), 2128-2129.
483. E. Ott, C. Grebogi, and J. A. Yorke, Controlling chaos, Phys. Rev. Lett., 64(1990), 1196-1199.
484. D. B. Owens, F. J. Capone, R. M. Hall, J. M. Brandon, and J. R. Chambers, Transonic free-to-roll analysis of abrupt wing stall on military aircraft, J. Aircraft, 41-3(2004), 474-484.
485. M. S. Padin, F. I. Robbio, J. L. Moiola, and G. R. Chen, On limit cycle approximations in the van der Pol oscillator, Chaos Solitons Fractals, 23(2005), 207-220.
486. F. Pasemann, A simple chaotic neuron, Phys. D, 104(1997), 205-211.
487. F. Pasemann, Driving neuromodules into synchronous chaos, in J. Mira and J. V. Sanchez-Andrés, eds., Foundations and Tools for Neural Modeling: International Work-Conference on Artificial and Natural Neural Networks (IWANN'99, Alicante, Spain, June 2-4, 1999) Proceedings, Vol. I, Lecture Notes in Computer Science, Vol. 1606, Springer-Verlag, Berlin, 1999, 377-384.
488. F. Paseman and N. Stollenwerk, Attractor switching by neural control of chaotic neurodynamics, Comput. Neural Systems, 9(1998), 549-561
489. L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., 64(1990), 821-824.
490. Y. Pei and H. Maoan, Twelve limit cycles in a cubic case of the 16th Hilbert problem, Internat. J. Bifurcation Chaos, 15(2005), 2191-2205.
491. H. Poincaré, Mémoire sur les courbes définies par une equation différentielle, J. Math., 7(1881), 375-422;
492. oeuvre, Gauthier-Villars, Paris, 1890.
493. P. Pokorny, I. Schreiber, and M. Marek, On the route to strangeness without chaos in the quasiperiodically forced van der Pol oscillator, Chaos Solitons Fractals, 7(1996), 409-424.
494. F. Rosenblatt, The perceptron: A probabalistic model for information storage and organization in the brain, Psychological Rev., 65(1958), 386-408.
495. M. T. Rosenstein, J. J. Collins, and C. J. Deluca, A practical method for calculating largest Lyapunov exponents from small data sets, Phys. D, 65-1-2(1993), 117-134.
496. O. E. Rössler, An equation for continuous chaos, Phys. Lett., 57A (1976), 397-398.
497. J. A. Rothwell, The word liar, New Scientist, March (2003), 51.
498. R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system, Phys. Rev. Lett., 68(1992), 1259-1262.
499. G. S. Rychkov, The maximum number of limit cycles of the system x = y - a0x - a1x - a2x, y = -x is two, Differentsial'nye Uravneniya, 11(1973), 380-391.
500. I.W. Sandberg, ed., J. T. Lo, C. L. Fancourt, J. Principe, S. Haykin, and S. Katargi, Nonlinear Dynamical Systems: Feedforward Neural Network Perspectives, Adaptive Learning Systems to Signal Processing, Communications, and Control, Wiley-Interscience, New York, 2001.
501. N. Sarkar and B. B. Chaudhuri, Multifractal and generalized dimensions of graytone digital images, Signal Process., 42(1995), 181-190.
502. S. J. Schiff, K. Jerger, D. H. Doung, T. Chang, M. L. Spano, and W. L.
503. Chao-Xiang Shi, Nonlinear fibre loop mirror with optical feedback, Optics Comm., 107(1994), 276-280.
504. T. Shinbrot, C. Grebogi, E. Ott, and J. A. Yorke, Using chaos to direct trajectories to targets, Phys. Rev. Lett., 65(1990), 3215-3218.
505. K. S. Sibirskii, The number of limit cycles in the neighbourhood of a critical point, Differential Equations, 1(1965), 36-47
506. V. Silberschmidt, Fractal and multifractal characteristics of propagating cracks, J. Phys. IV, 6(1996), 287-294.
507. J. Singer, Y.-Z. Wang, and H. H. Bau, Controlling a chaotic system, Phys. Rev. Lett., 66(1991), 1123-1125.
508. S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73(1967), 747-817.
509. P. W. Smith and E. H. Turner, A bistable Fabry-Perot resonator, Appl. Phys. Lett., 30(1977), 280-281.
510. S. D. Smith, Towards the optical computer, Nature, 307(1984), 315-316.
511. Shi Songling, A concrete example of the existence of four limit cycles for plane quadratic systems, Sci. Sinica A, 23(1980), 153-158.
512. H. F. Stanley and P. Meakin, Multifractal phenomena in physics and chemistry, Nature, 335(1988), 405-409.
513. A. L. Steele, S. Lynch, and J. E. Hoad, Analysisofoptical instabilities and bistability in a nonlinear optical fibre loop mirror with feedback, Optics Comm., 137(1997), 136-142.
514. A. Szöke, V. Daneu, J. Goldhar, and N. A. Kurnit, Bistable optical element and its applications, Appl. Phys. Lett., 15(1969), 376.
515. B. Van Der Pol, On relaxation oscillations, Philos. Magazine, 7(1926), 901-912, 946-954.
516. V. Volterra, Variazioni e fluttuazioni del numero d'individui in specie animali conviventi, Mem. R. Accad. Naz. Lincei, 2-3(1926), 30-111;
517. Mem. R. Com. Tolassogr. Ital., 431(1927), 1-142.
518. D. M. Wang, Polynomial systems from certain differential equations, J. Symbolic Comput., 28(1999), 303-315.
519. B. Widrow and M. E. Hoff, Adaptive switching circuits, in 1960 IRE WESCON Convention Record, Part 4, IRE, New York, 1960, 96-104.
520. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, Determining Lyapunov exponents from a time series, Phys. D, 16(1985), 285-317.
521. S. Yousefi, Y. Maistrenko, and S. Popovych, Complex dynamics in a simple model of interdependent open economies, Discrete Dynam. Nature Society, 5-3(2000), 161-177
522. X. H. Zhang and S. B. Zhou, Chaos synchronization for bi-directional coupled twoneuron systems with discrete delays, in J. Wang, X. Liao, and Z. Yi, eds., Advances in Neural Networks: ISNN 2005 (2nd International Symposium on Neural Networks, Chongqing, China, May 30-June 1, 2005) Proceedings, Part I, Lecture Notes in Computer Science, Vol. 3496, Springer-Verlag, New York, 2005, 351-356.
523. P. Zhou, X. H. Luo, and H. Y. Chen, A new chaotic circuit and its experimental results, Acta Phys. Sinica, 54-11(2005), 5048-5052.
524. H. Zoladek, Eleven small limit cyclesin a cubic vectorfield, Nonlinearity, 8(1995), 843-860.
525. M. Zoltowski, An adaptive reconstruction of chaotic attractors out of their single trajectories, Signal Process., 80-6(2000), 1099-1113