Elegant chaos: Algebraically simple chaotic flows

Elegant Chaos: Algebraically Simple Chaotic Flows

Volumn , Issue , 2010, Pages 1-285

  Sprott, Julien Clinton ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

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[No Author keywords available]

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EID: 84967350878     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/7183     Document Type: Book

References (318)

1. Ablowitz, M. J. (1991). Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University Press, Cambridge).
2. Abraham, R. and Ueda, Y. (2000). The Chaos Avant-Garde: Memories of the Early Days of Chaos Theory World Scientific, Singapore
3. Abramowitz, M. and Stegun, I. A. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York).
4. Afraimovich, V. H. and Lin, W. W. (1998). Synchronization in lattices of coupled oscillators with Neumann periodic boundary conditions, Dynam. Stabil. Syst.13, pp. 237-264.
5. Aguirre, J., Viana, R. L., and Sanjuan, M. A. F. (2009). Fractal structures in nonlinear dynamics, Rev. Mod. Phys.81, pp. 333-386.
6. Ahmad, W. M. (2006). A simple multi-scroll hyperchaotic system, Chaos, Solitons Fractals27, pp. 1213-1219.
7. Allan, D. W. (1962). On the behaviour of systems of coupled dynamos, Math. Proc. Camb. Phil. Soc.58, pp. 671-693.
8. Alvarez-Ramirez, J., Delgado-Fernandez, J. and Espinosa-Paredes, G. (2005). The origin of a continuous two-dimensional “chaotic” dynamics, Int. J. Bifurcat. Chaos Appl. Sci. Eng.15, pp. 3023-3029.
9. Amari, S., Yoshida, K., and Kanatani, K. (1977). A mathematical foundation for statistical neurodynamics, SIAM J. Appl. Math.33, pp. 95-126.
10. an der Heiden, U. and Mackey, M. C. (1982). The dynamics of production and destruction: Analytic insight into complex behavior, J. Math. Biol.16, pp. 75-101.
11. Anishchenko, V. S. and Strelkova, G. I. (1997). Attractors of dynamical systems. In Control of Oscillations and Chaos, Proceedings, 1997 International Conference, Vol. 3, pp. 498-503.
12. Antoniou, A. (1969). Realisation of gyrators using OpAmps and their use in RC-active network synthesis, Proc. IEE116, pp. 1838-1850.
13. Arneodo, A., Coullet, P., and Tresser, C. (1980). Occurence of strange attractors in three-dimensional Volterra equations, Phys. Lett. A79, pp. 259-263.
14. Arneodo, A., Coullet, P., and Tresser, C. (1981). A possible mechanism for the onset of turbulence, Phys. Lett. A81, pp. 197-201.
15. Arneodo, A., Coullet, P., and Tresser, C. (1982). Oscillators with chaotic behavior: An illustration of a theorem by Shilnikov, J. Stat. Phys.27, pp. 171-182.
16. Arnold, V. I. (1978). Mathematical Methods of Classical Mechanics(Springer, New York).
17. Arulgnanam, A., Thamilmaran, K., and Daniel, M. (2009). Chaotic dynamics with high complexity in a simplified new nonautonomous nonlinear electronic circuit, Chaos, Solitons Fractals42, pp. 2246-2253.
18. Auvergne, M. and Baglin, A. (1985). A dynamical instability as a driving mechanism for stellar oscillations, Astron. Astrophys.142, pp. 388-392.
19. Baker, G. L. and Blackburn, J. A. (2005). The Pendulum: A Case Study in Physics(Oxford University Press, Oxford).
20. Baker, G. L. and Gollub, J. P. (1996). Chaotic Dynamics: An Introduction(2nd edn) (Cambridge University Press, Cambridge).
21. Bartuccelli, M. V., Deane, J. H. B., and Gentile, G. (2007). Bifurcation phenomena and attractive periodic solutions in the saturating inductor circuit, Proc. Math. Phys. Eng. Sci.463, pp. 2351-2369.
22. Battelino, P. M., Grebogi, C., Ott, E., and Yorke, J. A. (1988). Multiple coexisting attractors, basin boundaries and basic sets, Phys. Nonlinear Phenom.32, pp. 296-305.
23. Becker, T. and Weispfenning, V. (1993). Grobner Bases: A Computational Approach to Commutative Algebra(Springer, New York).
24. Bellen, A. and Zennaro, M. (2003). Numerical Methods for Delay Differential Equations(Oxford University Press, Oxford).
25. Bernhardt, P. A. (1991). The autonomous chaotic relaxation oscillator: An electrical analogue to the dripping faucet, Phys. Nonlinear Phenom.52, pp. 489-527.
26. Bilotta, E. and Pantano, P. (2008). A Gallery of Chua Attractors(World Scientific, Singapore).
27. Birkhoff, G. and Rota, G. C. (1978). Ordinary Differential Equations(3rd edn) (Wiley, New York), pp. 134.
28. Bonatto, C. and Gallas, J. A. C. (2008). Periodicity hub and nested spirals in the phase diagram of a simple resistive circuit, Phys. Rev. Lett.101, pp. 054101-1-4.
29. Bonatto, C., Gallas, J. A. C., and Ueda, Y. (2008). Chaotic phase similarities and recurrences in a damped-driven Duffing oscillator, Phys. Rev. E77, pp. 026217-1-5.
30. Bondi, H. (1957). Negative mass in general relativity, Rev. Mod. Phys.29, pp. 423-428.
31. Bonhoeffer, K. F. (1953). Modelle der Nervenerregung, Naturwissenschaften40, pp. 301-311.
32. Brayton, R. K. (1966). Bifurcation of periodic solutions in a nonlinear difference-differential equation of neutral type, Q. Appl. Math.24, 215-224.
33. Brown, R. (1993). From Chua’s circuit to the generalized Chua map, J. Circ. Syst. Comput.3, pp. 11-32.
34. Brummitt, C. D. and Sprott, J. C. (2009). A search for the simplest chaotic partial differential equation, Phys. Lett. A373, pp. 2717-2721.
35. Bullard, E. (1955). The stability of a homopolar dynamo, Math. Proc. Camb. Phil. Soc.51, pp. 744-760.
36. Cafagna, D. and Grassi, G. (2003). Hyperchaotic coupled Chua circuits: An approach for generating new n x m-scroll attractors, Int. J. Bifurcat. Chaos Appl. Sci. Eng.13, pp. 2537-2550.
37. Camacho, E., Rand, R., and Howland, H. (2004). Dynamics of two van der Pol oscillators coupled via a bath, Int. J. Solid. Struct.41, pp. 2133-2143.
38. Canuto, C., Hussani, M. Y., Quarteroni, A., and Zang, T. A. (2006). Spectral Methods: Fundamentals in Single Domains(Springer-Verlag, Berlin).
39. 2)x + y = bXkcos (Xt + k)large, J. Lond. Math. Soc.20, pp. 180-189.
40. Cartwright, J. H. E., Hernandez-Garcia, E., and Piro, O. (1997). Burridge-Knopoff models as elastic excitable media, Phys. Rev. Lett.79, pp. 527-530.
41. Case, W. B. (1996). The pumping of a swing from the standing position, Am. J. Phys.64, pp. 215-220.
42. Case, W. B. and Swanson, M. A. (1990). The pumping of a swing from the seated position, Am. J. Phys.58, pp. 463-467.
43. Chen, F. F. (1984). Introduction to Plasma Physics and Controlled Fusion(2nd edn) (Plenum Press, New York).
44. Chen, G. and Ueta, T. (1999). Yet another chaotic attractor, Int. J. Bifurcat. Chaos Appl. Sci. Eng.9, pp. 1465-1466.
45. Chen, Z., Yang, Y., Qi, G., and Yuan, Z. (2007). A novel hyperchaos system only with one equilibrium, Phys. Lett. A360, pp. 696-701.
46. Chirikov, B. V. (1979). A universal instability of many-dimensional oscillator systems, Phys. Rep.52, pp. 263-379.
47. Chiu, C. H., Lin, W. W., and Wang, C. S. (2001). Synchronization in lattices of coupled oscillators with various boundary conditions, Nonlinear Anal. Theor. Meth. Appl.46, pp. 213-229.
48. Chlouverakis, K. E. and Sprott, J. C. (2006). Chaotic hyperjerk systems, Chaos, Solitons Fractals28, pp. 739-746.
49. Chlouverakis, K. E. and Sprott, J. C. (2007). Hyperlabyrinth chaos: From chaotic walks to spatiotemporal chaos, Chaos17, pp. 023110-1-8.
50. Chua, L. O. (1992). The genesis of Chua’s circuit, Archiv fur Elektronik und Ubertragungstechnik46, pp. 250-257.
51. Chua, L. O. (1994). Chua’s circuit: Ten years later, IEICE Trans. Fund. Electron. Comm. Comput. Sci. E77-A, pp. 1811-1822.
52. Chua, L. O., Hasler, M., Neirynck, J., and Verburgh, P. (1982). Dynamics of a piecewise-linear resonant circuit, IEEE Trans. Circ. Syst.29, pp. 535-547.
53. Chua, L. O., Komuro, M., and Matsumoto, T. (1986). The double scroll family, IEEE Trans. Circ. Syst.33, pp. 1073-1118.
54. Cook, A. E. and Roberts, P. H. (1970). The Rikitake two disk dynamo system, Math. Proc. Camb. Phil. Soc.68, pp. 547-569.
55. Coullet, P., Tresser, C., and Arneodo, A. (1979). Transition to stochasticity for a class of forced oscillators, Phys. Lett. A72, pp. 268-270.
56. Cryer, C. W. (1972). Numerical methods for functional differential equations. In Delay and Functional Differential Equations and their Applications(ed. K. Schmitt), pp. 17-101 (Academic Press, New York).
57. Cummings, F. W., Dixon, D. D., and Kaus, P. E. (1992). Dynamical model of the magnetic field of neutron stars, Astrophys. J.386, pp. 215-221.
58. Darrigol, O. (2003). The spirited horse, the engineer, and the mathematician: Water waves in nineteenth-century hydrodynamics, Archive for History of Exact Sciences58, pp. 21-95.
59. Dean, J. H. B. (1994). Modeling the dynamics of nonlinear inductor circuits, IEEE Trans. Magn.30, pp. 2795-2801.
60. Den Hartog, J. P. (1930). Forced vibrations with combined viscous and Coulomb damping, Phil. Mag.9, pp. 801-817.
61. Ditto, W. L., Spano, M. L., Savage, H. T., Rauseo, S. N., Heagy, J., and Ott, E. (1990). Experimental observation of a strange nonchaotic attractor, Phys. Rev. Lett.65, pp. 533-536.
62. Dixon, D. D., Cummings, F. W., and Kaus, P. E. (1993). Continuous “chaotic” dynamics in two dimensions, Phys. Nonlinear Phenom65, pp. 109-116.
63. Drazin, P. G. and Johnson, R. S. (1989). Solitons: An Introduction(Cambridge University Press, Cambridge).
64. Driver, R. D. (1984). A neutral system with state dependent delay, J. Differ. Equal.54, pp. 73-86.
65. Duan, Z., Wang, J.-Z., and Huang, L. (2005). Attraction/repulsion functions in a new class of chaotic systems, Phys. Lett. A335, pp. 139-149.
66. Duffing, G. (1918). Erzwungene Schwingungen bei Veranderlicher Eigenfrequenz und ihre Technische Bedeutung, Sammlung Vieweg, Heft 41/42(Vieweg, Braunschweig).
67. Earnshaw, S. (1842). On the nature of the molecular forces which regulate the constitution of the luminiferous ether, Trans. Camb. Phil. Soc.7, pp. 97-112.
68. Eichhorn, R., Linz, S. J., and Hanggi, P. (1998). Transformations of nonlinear dynamical systems to jerky motion and its application to minimal chaotic flows, Phys. Rev. E58, pp. 7151-7164.
69. Eichhorn, R., Linz, S. J., and Hanggi, P. (2002). Simple polynomial classes of chaotic jerky dynamics, Chaos, Solitons Fractals13, pp. 1-15.
70. Elwakil, A. S. and Kennedy, M. P. (1998). High frequency Wien-type chaotic oscillator, Electron. Lett.34, pp. 1161-1162.
71. Elwakil, A. S. and Kennedy, M. P. (2001). Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices, IEEE Trans. Circ. Syst.48, pp. 289-307.
72. Elwakil, A. S. and Solimon, A. M. (1997). A family of Wien type oscillators modified for chaos, Int. J. Circuit Theory Appl.25, pp. 561-579.
73. Elwakil, A. S., Salama, K. N., and Kennedy, M. P. (2000). A system for chaos generations and its implementation in monolithic form, IEEE Trans. Circ. Syst.47, pp. 217-220.
74. Elwakil, A. S., Ozoguz, S., and Kennedy, M. P. (2002). Creation of a complex butterfly attractor using a novel Lorenz-type system, IEEE Trans. Circ. Syst.49, pp. 527-530.
75. Erneux, T. (2009). Applied Delay Differential Equations, Surveys and Tutorials in the Applied Mathematical Sciences (Springer, New York).
76. Farmer, J. D. (1982). Chaotic attractors of an infinite dimensional system, Phys. Nonlinear Phenom.4, pp. 366-393.
77. Farmer, J. D. (1985). Sensitive dependence on parameters in nonlinear dynamics, Phys. Rev. Lett.55, pp. 351-354.
78. Feeny, B. (1992). A nonsmooth Coulomb friction oscillator, Phys. Nonlinear Phenom.59, pp. 25-38.
79. Feeny, B. and Moon, F. C. (1994). Chaos in a forced dry-friction oscillator: Experiments and numerical modeling, J. Sound Vib.170, pp. 303-323.
80. Feudel, U. and Grebogi, C. (2003). Why are chaotic attractors rare in multistable systems?, Phys. Rev. Lett.91, pp. 134102-1-4.
81. Feudel, U., Grebogi, C., Hunt, B. R., and Yorke, J. A. (1996). Map with more than 100 coexisting low-period periodic attractors, Phys. Rev. E54, pp. 71-81.
82. Feudel, U., Kuznetsov, S., and Pikovsky, A. (2006). Strange Nonchaotic Attractors (World Scientific, Singapore).
83. FitzHugh, R. (1960). Thresholds and plateaus in the hodkin-huxley nerve equations, J. Gen. Physiol.43, pp. 867-896.
84. FitzHugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane, Biophys. J.1, pp. 445-446.
85. Flaherty, J. E. and Hoppensteadt, F. C. (1978). Frequency entrainment of a forced van der Pol oscillator, Stud. Appl. Math.58, pp. 500-544.
86. Fortuna, L., Frasca, M., and Xibilia, M. G. (2009). Chua’s Circuit Implementations: Yesterday, Today and Tomorrow(World Scientific, Singapore).
87. Funahashi, K. and Nakamura, Y. (1993). Approximation of dynamical systems by continuous time recurrent neural networks, Neural Networks 6, pp. 801-806.
88. Gans, R. F. (1995). When is cutting chaotic?, J. Sound Vib.188, pp. 75-83.
89. Gao, T., Chen, G., Chen, Z., and Cang, S. (2007). The generation and circuit implementation of a new hyper-chaos based upon Lorenz system, Phys. Lett. A361, pp. 78-86.
90. Gear, C. W. (1971). Numerical Initial Value Problems in Ordinary Differential Equations(Prentice Hall, Englewood Cliffs, NJ).
91. Geist, K., Parlitz, U., and Lauterborn, W. (1990). Comparison of different methods for computing Lyapunov exponents, Prog. Theor. Phys.83, pp. 875-893.
92. Gerjuoy, E. (1949). On Newton’s third law and the conservation of momentum, Am. J. Phys.17, pp. 477-482.
93. Gilmore, R. and Letellier, C. (2007). The Symmetry of Chaos(Oxford University Press, Oxford).
94. Gleick, J. (1987). Chaos: Making a New Science(Viking, New York).
95. Gollub, J. P., Brunner, T. O., and Danly, B. G. (1978). Periodicity and chaos in coupled nonlinear oscillators, Science200, pp. 48-50.
96. Gonzaiez-Miranda, J. M. (2006). Highly incoherent phase dynamics in the Sprott E chaotic flow, Phys. Lett. A352, pp. 83-88.
97. Gottlieb, H. P. W. (1996). Question 38. What is the simplest jerk function that gives chaos?, Am. J. Phys.64, pp. 525.
98. Gottlieb, H. P. W. and Sprott, J. C. (2001). Simplest driven conservative chaotic oscillator, Phys. Lett. A291, pp. 385-388.
99. Grantham, W. J. and Lee, B. (1993). A chaotic limit cycle paradox, Dynam. Contr.3, pp. 159-173.
100. Grassberger, P. and Procaccia, I. (1984). Dimensions and entropies of strange attractors from fluctuating dynamics approach, Phys. Nonlinear Phenom. 13, pp. 34-54.
101. Grebogi, C., Ott, E. Pelikan, S. and Yorke J. A. (1984). Strange attractors that are not chaotic, Phys. Nonlinear Phenom.13, pp. 261-268.
102. Grebogi, C., McDonald, S. W., Ott, E., and Yorke, J. A. (1985). Exterior dimension of fat fractals, Phys. Lett. A110, pp. 1-4.
103. Gutzwiller, M. C. (1998). Moon-Earth-Sun: The oldest three-body problem, Rev. Mod. Phys.70, pp. 589-639.
104. Gyergyek, T., Cercek, M., and Stanojevic, M. (1997). Experimental evidence of periodic pulling in a weakly magnetized discharge plasma column, Contrib. Plasma Phys.37, pp. 399-416.
105. Hale, J. K. (1977). Theory of Functional Differential Equations(Springer, New York).
106. Hayashi, C., Ueda, Y., Akamatsu, N., and Itakura, H. (1970). On the behavior of self-oscillatory systems with external force (in Japanese), Trans. Inst. Electron. Comm. Eng. Jpn. 53-A, pp. 150-158.
107. Haykin, S. (1999). Neural Networks - A Comprehensive Foundation(2nd edn) (Prentice Hall, Upper Saddle River, NJ).
108. Heidel, J. and Zhang, F. (1999). Nonchaotic behaviour in three-dimensional quadratic systems II. The conservative case, Nonlinearity12, pp. 617-633.
109. Heidel, J. and Zhang, F. (2007). Nonchaotic and chaotic behavior in threedimensional quadratic systems: Five-one conservative cases, Int. J. Bifur-cat. Chaos Appl. Sci. Eng.17, pp. 2049-2072.
110. Henon, M. (1982). On the numerical computation of Poincare maps, Phys. Nonlinear Phenom.5, pp. 412-414.
111. Henon, M. and Heiles, C. (1964). The applicability of the third integral of motion: Some numerical experiments, Astrophys. J.69, pp. 73-79.
112. Hirsch, M. W. (1988). Systems of differential equations which are competitive or cooperative III: Competing species, Nonlinearity1, pp. 51-71.
113. Hirsch, M. W., Smale, S., and Devaney, R. L. (2004). Dynamical Systems, and an Introduction to Chaos(2nd edn) (Elsevier/Academic Press, Amsterdam).
114. Hodgkin, A. and Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitatiion in nerve, J. Physiol. 117, pp. 500-544.
115. Hoover, W. G. (1995). Remark on ‘Some simple chaotic flows,’ Phys. Rev. E51, pp. 759-760.
116. Horowitz, P. and Hill, W. (1989). The Art of Electronics(2nd edn) (Cambridge University Press, Cambridge).
117. Horton, W., Weigel, R. S., and Sprott, J. C. (2001). Chaos and the limits of predictability for the solar-wind-driven magnetosphere-ionosphere system, Phys. Plasmas8, pp. 2946-2952.
118. Hoshi, M. and Kono, M. (1988). Rikitake two-disk dynamo system: Statistical properties and growth of instability, J. Geophys. Res.93, pp. 11643-11654.
119. Hutchinson, G. E. (1948). Circular causal mechanisms in ecology, Ann. New York Acad. Sci.50, pp. 221-246.
120. Ikeda, K. (1979). Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system, J. Opt. Comm.30, pp. 257-261.
121. Ikeda, K. and Matsumoto, K. (1987). High-dimensional chaotic behavior in systems with time-delayed feedback, Phys. Nonlinear Phenom.29, pp. 223-235.
122. Innocenti, G., Genesio, R., and Ghilardi, C. (2008). Oscillations and chaos in simple quadratic systems, Chaos18, pp. 1917-1937.
123. Ito, K. (1980). Chaos in the Rikitake two-disc dynamo system, Earth Planet. Sci. Lett.51, pp. 451-456.
124. Jackson, E. A. and Kodogeorgiou, A. (1992). A coupled Lorenz-cell model of Rayleigh-Benard turbulence, Phys. Lett. A168, pp. 270-275.
125. Jia, Q. (2007). Hyperchaos generated from the Lorenz chaotic system and its control, Phys. Lett. A366, pp. 217-222.
126. Josic, K. and Wayne, C. E. (2000). Dynamics of a ring of diffusively coupled Lorenz oscillators, J. Stat. Phys.98, pp. 1-30.
127. Kapitaniak, T. and Chua, L. O. (1994). Hyperchaotic attractors of unidirectionally-coupled Chua’s circuits, Int. J. Bifurcat. Chaos Appl. Sci. Eng.4, pp. 477-482.
128. Kaplan, J. and Yorke, J. (1979). Chaotic behavior of multidimensional difference equations. In Functional Differential Equations and Approximation of Fixed Points, Lecture Notes in Mathematics, Vol. 730 (ed. H. -O. Peitgen and H. -O. Walther), pp. 228-237 (Springer, Berlin).
129. Keller, J. M. (1942). Newton’s third law and electrodynamics, Am. J. Phys.10, pp. 1005-1017.
130. Kennedy, M. P. (1992). Robust op amp realization of Chua’s circuit, Frequenz 46, pp. 66-80.
131. Kevrekidis, I. G., Nicolaenko, B., and Scovel, J. C. (1990). Back in the saddle again: A computer assisted study of the Kuramoto-Sivashinsky equation, SIAM J. Appl. Math.50, pp. 760-790.
132. Khibnik, A. I., Roose, D., and Chua, L. O. (1993). On periodic orbits and homoclinic bifurcations in Chua’s circuit with a smooth nonlinearity, Int. J. Bifurcat. Ch, ao.s Appl. Sci. Eng.3, pp. 363-384.
133. Kiers, K., Klein, T., Kolb, J., Price, S., and Sprott, J. C. (2004a). Chaos in a nonlinear analog computer, Int. J. Bifurcat. Chaos Appl. Sci. Eng.14, pp. 2867-2873.
134. Kiers, K., Schmidt, D., and Sprott, J. C. (2004b). Precision measurements of a simple chaotic circuit, Am. J. Phys.72, pp. 503-509.
135. Kilic, R. and Yildirim, F. (2008). A survey of Wien bridge-based chaotic oscillators: Design and experimental issues, Chaos, Solitons Fractals38, pp. 1394-1410.
136. Kitchens, B. P. (1998). Symbolic Dynamics: One-sided, Two-sided and Countable State Markov Shifts(Springer Universitext, Berlin).
137. Kolmanovski, V. and Myshkis, A. (1999). Introduction to the Theory and, Applications of Functional Differential Equations(Kluwer Academic Publishers, Dordrecht).
138. Korteweg, D. J. and de Vries, G. (1895). On the change of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Phil. Mag. (Series 5) 39, pp. 422-433.
139. Krogdahl, W. S. (1955). Stellar pulsation as a limit-cycle phenomenon, Astrophys. J.122, pp. 43-51.
140. Kuang, Y. (1993). Delay Differential Equations with Applications in Population Dynamics(Academic Press, San Diego).
141. Kudryashov, N. A. (1990). Exact solutions of the generalized Kuramoto-Sivashinsky equation, Phys. Lett. A147, pp. 287-291.
142. Kuramoto, Y. and Tsuzuki, T. (1976). Persistent propagation of concentration waves in dissipative media far from thermal equilibium, Progr. Theor. Phys. 55, pp. 356-369.
143. Kuznetsov, Y. A. (1995). Elements of Applied Bifurcation Theory(2nd edn) (Springer, New York).
144. Lainscsek, C., Lettellier, C., and Gorodnitsky, I. (2003). Global modeling of the Rossler system from the ^-variable, Phys. Lett. A314, pp. 409-427.
145. Laje, R., Gardner, T., and Mindlin, G. B. (2001). Continuous model for vocal fold oscillations to study the effect of feedback, Phys. Rev. E 64, pp. 056201-1-7
146. Laskar, J. (1989). A numerical experiment on the chaotic behaviour of the Solar System, Nature338, pp. 237-238.
147. Lax, P. and Levermore, C. D. (1983). The small dispersion limit of the Korteweg-de Vries equation, Part I, II, III, Comm. Pure App. Math.36, pp. 253-290, 809-830 571-593,.
148. Leipnik, R. B. and Newton, T. A. (1979). Double strange attractors in rigid body motion with linear feedback control, Phys. Lett. A86, pp. 63-67.
149. Letellier, C. and Valee, O. (2003). Analytical results and feedback circuit analysis for simple chaotic flows, J. Phys. Math. Gen.36, pp. 11229-11245.
150. Levi, M. (1981). Qualitative analysis of the periodically forced relaxation oscillations, Memoir. Am. Math. Soc.214, pp. 1-147.
151. Levinson, N. (1949). A second order differential equation with singular solutions, Ann. Math.50, pp. 127-153.
152. Li, Y. C. (2004). Chaos in Partial Differential Equations(International Press, Somerville, MA).
153. Li, T. -Y. and Yorke, J. A. (1975). Period three implies chaos, Am. Math. Mon. 82, pp. 985-992.
154. Li, Y., Tang, W. K. S., Chen, G. (2005a). Generating hyperchaos via state feedback control, Int. J. Bifurcat. Chaos Appl. Sci. Eng.15, pp. 3367-3375.
155. Li, Y., Tang, W. K. S., Chen, G. (2005b). Hyperchaos evolved from the generalized Lorenz equation, Int. J. Circ. Theor. Appl.33, pp. 235-251.
156. Lichtenberg, A. J. and Lieberman, M. A. (1992). Regular and Chaotic Dynamics (2nd edn), Applied Mathematical Sciences, Vol. 38(Springer, New York).
157. Lin, C. D. (1995). Hyperspherical coordinate approach to atomic and other Coulombic three-body systems, Phys. Rep.257, pp. 1-83.
158. Lind, D. and Marcus, B. (1995). An Introduction to Symbolic Dynamics and Coding(Cambridge University Press, Cambridge).
159. Linsay, P. S. (1981). Period doubling and chaotic behavior in a driven anharmonic oscillator, Phys. Rev. Lett.19, pp. 1349-1352.
160. Linz, S. J. (1997). Nonlinear dynamical models and jerky motion, Am. J. Phys. 65, pp. 523-526.
161. Linz, S. J. (2000). No-chaos criteria for certain jerky dynamics, Phys. Lett. A 275, pp. 204-210.
162. Linz, S. J. (2008). On hyperjerky systems, Chaos, Solitons Fractals37, pp. 741-747.
163. Linz, S. J. and Sprott, J. C. (1999). Elementary chaotic flow, Phys. Lett. A259, pp. 240-245.
164. Liu, W. and Chen, G. (2003). A new chaotic system and its generation, Int. J. Bifurcat. Chaos Appl. Sci. Eng.13, pp. 261-267.
165. Liu, Z. Lai, Y. C., and Matias, M. A. (2003). Universal scaling of Lyapunov exponents in coupled chaotic oscillators, Phys. Rev. E67, pp. 045203(R)-1-4.
166. Lorenz, E. N. (1963). Deterministic nonperiodic flow, J. Atmos. Sci.20, pp. 130-141.
167. Lorenz, E. N. (1991). Dimension of weather and climate attractors, Nature353, pp. 241-244.
168. Lorenz, E. N. (1993). The Essence of Chaos(University of Washington Press, Seattle).
169. Lorenz, E. N. and Emanuel, K. A. (1998). Optimal sites for supplementary weather observations: Simulation with a small model, J. Atmos. Sci.55, pp. 399-414.
170. Losson, J., Mackey, M. C., and Longtin, A. (1993). Solution multistability in first-order nonlinear differential delay equations, Chaos3, pp. 167-176.
171. Lotka, A. J. (1925). Elements of Physical Biology(Williams and Wilkins, Baltimore).
172. Low, L. A., Reinhall, P. G., and Storti, D. W. (2003). An investigation of coupled van der Pol oscillators, J. Vib. Acoust.125, pp. 162-169.
173. Lu, J. and Chen, G. (2006). Generating multiscroll chaotic attractors: Theories, methods and applications, Int. J. Bifurcat. Chaos Appl. Sci. Eng.16, pp. 775-858.
174. Lu, H. and He, Z. (1996). Chaotic behavior in first-order autonomous continuoustime systems with delay, IEEE Trans. Circ. Syst.43, pp. 700-702.
175. Lu, H., He, Y., and He, Z. (1998). A chaos-generator: Analyses of complex dynamics of a cell equation in delayed cellular neural networks, IEEE Trans. Circ. Syst.45, pp. 178-181.
176. LU, J., Chen, G., Cheng, D., and Celikovsky, S. (2002). Bridge the gap between the Lorenz system and the Chen system, Int. J. Bifurcat. Chaos Appl. Sci. Eng.12, pp. 2917-2926.
177. Maartens, R., Lesame, W. M., and Ellis, G. F. R. (1998). Newtonian-like and anti-Newtonian universes, Classical Quant. Grav.15, pp. 1005-1017.
178. Mackey, M. C. and Glass, L. (1977). Oscillation and chaos in physiological control systems, Science197, pp. 287-289.
179. Mahla, A. I. and Badan Palhares, A. G. (1993). Chua’s circuit with a discontinuous nonlinearity, J. Circ. Syst. Comput.3, pp. 231-237.
180. Mahmoud, G. M. and Bountis, T. (2004). The dynamics of systems of complex nonlinear oscillators: A review, Int. J. Bifurcat. Chaos Appl. Sci. Eng.14, pp. 3821-3846.
181. Malasoma, J. -M. (2000). What is the simplest dissipative chaotic jerk equation which is parity invariant?, Phys. Lett. A264, pp. 383-389.
182. Malasoma, J. -M. (2002). A new class of minimal chaotic flows, Phys. Lett. A 305, pp. 52-58.
183. Mandelbrot, B. B. (1983). The Fractal Geometry of Nature(Freeman, New York).
184. Marchal, C. (1990). Three-Body Problem(Elsevier, Amsterdam)
185. Marcus, C. M. and Westervelt, R. M. (1989). Stability of analog neural networks with delay, Phys. Rev. A39, pp. 347-349.
186. Marshall, D. and Sprott, J. C. (2009) Simple driven chaotic oscillators with complex variables, Chaos19, pp. 013124-1-7.
187. Matsumoto, T., Chua, L. O., and Komuro, M. (1985). The double scroll, IEEE Trans. Circ. Syst.33, pp. 797-818.
188. May, R. M. (1975). Stability and Complexity in Model Ecosystems(2nd edn) (Princeton University Press, Princeton, NJ).
189. McArthur, R. H. (1970). Species packing and competitive equilibrium for many species, Theor. Popul. Biol.1, pp. 1-11.
190. Moffat, H. K. (1979). A self-consistent treatment of simple dynamo systems, Geophys. Astrophys. Fluid Dynam.14, pp. 147-166.
191. Moon, F. C. and Holmes, W. T. (1979). A magnetoelastic strange attractor, J. Sound Vib.65, pp. 275-296.
192. Moore, D. W. and Spiegel, E. A. (1966). A thermally excited non-linear oscillator, Astrophys. J.143, pp. 871-887.
193. Morgul, O (1995). Inductorless realisation of chua oscillator, Electron. Lett.31, pp. 1303-1304.
194. Munmuangsaen, B. and Srisuchinwong, B. (2009). A new five-term simple chaotic attractor, Phys. Lett. A373, pp. 4038-4043.
195. Murali, K., Lakshmanan, M., and Chua, L. O. (1994). Bifurcation and chaos in the simplest dissipative non-autonomous circuit, Int. J. Bifur. Chaos Appl. Sci. Eng.4, pp. 1511-1524.
196. Nagumo, J., Arimoto, S., and Yoshizawa, S. (1962). An active pulse transmission line simulating nerve axon, Proc. Inst. Radio Eng.50, pp. 2061-2070.
197. Namajunas, A. and Tamasevicius, A. (1995). Modified Wien-bridge oscillator for chaos, Electron. Lett.31, pp. 335-336.
198. Namajunas, A., Pyragas, K., and Tamasevicius, A. (1995). An electronic analog of the Mackey-Glass system, Phys. Lett. A201, pp. 42-46.
199. Nelson, P. W. and Perelson, A. S. (2002). Mathematical analysis of delay differential equation models of HIV-1 infection, Math. Biosci.179, pp. 73-94.
200. Ning, C. and Haken, H. (1990). Detuned lasers and the complex Lorenz equations: Subcritical and supercritical Hopf bifurcations, Phys. Rev. A41, pp. 3826-3837.
201. Nishio, Y., Inaba, N., Mori, S., and Saito, T. (1990). Rigorous analysis of windows in a symmetric circuit, IEEE Trans. Circ. Syst.37, pp. 473-487.
202. Nose, S. (1991). Constant temperature molecular dynamics methods, Prog. Theor. Phys. Suppl.103, pp. 1-46.
203. Ozoguz, S., Elwakil, A. S., and Salama, K. N. (2002). n-scroll chaos generator using nonlinear transconductors, Electron. Lett.38, pp. 685-686.
204. Passos, D. and Lopes, I. (2008). Phase space analysis: The equilibrium of the solar magnetic cycle, Solar Phys.250, pp. 403-410.
205. Pastor, I., Perez-Garcla, V. M., Encinas-Sanz, F., and Guerra, J. M. (1993). Ordered and chaotic behavior of two van der Pol oscillators, Phys. Rev. E 48, pp. 171-182.
206. Pastor-Diaz, I and Lopez-Fraguas, A. (1995). Dynamics of two coupled van der Pol oscillators, Phys. Rev. E52, pp. 1480-1489.
207. Patidar, V. and Sud, K. K. (2005). Bifurcation and chaos in simple jerk dynamical systems, Pramana - Journal of Physics64, pp. 75-93.
208. Pauli, W. (1922). Uber das modell des wasserstoffmolekulions, Ann. Phys.68, pp. 177-240.
209. Pesin, Y. B. and Sinai, Y. G. (1991). Space-time chaos in chains of weakly hyperbolic mappings, Advances in Soviet Math.3, pp. 165-168.
210. Peters, R. D. and Pritchett, T. (1997). The not-so-simple harmonic oscillator, Am. J. Phys.65, pp. 1067-1073.
211. Poincare, H. (1890). Sur le probleme des trois corps et les equations de la dy-namique, Acta. Math.13, pp. 1-270.
212. Pomeau, Y. and Manneville, P. (1980). Intermittent transition to turbulence in dissipative dynamical systems, Comm. Math. Phys.74, pp. 189-197.
213. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing(3rd edn) (Cambridge University Press, Cambridge).
214. Qi, G., Du, S., Chen, G., Chen, Z., and Yuan, Z. (2005). On a four dimensional chaotic system, Chaos, Solitons Fractals23, pp. 1671-1682.
215. Qi, G., van Wyk, M. A., van Wyk, B. J., and Chen, G. (2008). On a new hyperchaotic system, Phys. Lett. A372, pp. 124-136.
216. Rand, R. H. and Holmes, P. J. (1980). Bifurcation of periodic motions in two weakly coupled van der Pol oscillators, Int. J. Non. Lin. Mech.15, pp. 387-399.
217. Richards, R. (1999). The subtle attraction: Beauty as a force in awareness, creativity, and survival. In Affect, Creative Experience, and Psychological Adjustment(ed. S. W. Russ), pp. 195-219 (Brunner/Mazel, Philadelphia).
218. Rikitake, T. (1958). Oscillations of a system of disk dynamos, Math. Proc. Camb. Phil. Soc.54, pp. 89-105.
219. Rollins, R. W. and Hunt, E. R. (1982). Exactly solvable model of a physical system exhibiting universal chaotic behavior, Phys. Rev. Lett.69, pp. 1295-1298.
220. Rossler, O. E. (1976). An equation for continuous chaos, Phys. Lett. A57, pp. 397-398.
221. Rossler, O. E. (1979a). Continuous chaos - four prototype equations, Ann. New York Acad. Sci.316, pp. 376-392.
222. Rossler, O. E. (1979b). An equation for hyperchaos, Phys. Lett. A71, pp. 155-157.
223. Rowat, P. F. and Selverston, A. I. (1993). Modeling the gastric mill central pattern generator of the lobster with a relaxation-oscillator network, J. Neurophysiol.70, pp. 1030-1053.
224. Rowlands, G. and Sprott, J. C. (2008). A simple diffusion model showing anomalous scaling, Phys. Plasmas15, pp. 082308-1-7.
225. Ruby, L. (1996). Applications of the Mathieu equation, Am. J. Phys.64, pp. 39-44.
226. Rucklidge, A. M. (1992). Chaos in models of double convection, J. Fluid Mech. 237, pp. 209-229.
227. Ruelle, D. (1976). A measure associated with axiom A attractors, Am. J. Math. 98, pp. 619-654.
228. Russell, J. S. (1834). Notice of the reduction of an anomalous fact in hydrodynamics, and a new law of resistance to the motion of floating bodies, Rep. Br. Assoc. Adv. Sci., pp. 531-544.
229. Saltzman, B. (1962). Finite amplitude free conection as an initial value problem-I, J. Atmos. Sci.19, pp. 329-341.
230. Scheffczyk, C., Parlitz, U., Kurz, T., Knop, W., and Lauterborn, W. (1991). Comparison of bifurcation structures of driven dissipative nonlinear oscillators, Phys. Rev. E43, pp. 6495-6502.
231. Schiesser, W. E. (1991). The Numerical Method of Lines: Integration of Partial Differential Equations(Academic Press, San Diego).
232. Schiesser, W. E. and Griffiths, G. W. (2009). A Compendium of Partial Differential Equation Models: Method of Lines Analysis with Matlab(Cambridge University Press, Cambridge).
233. Schot, S. H. (1978). The time rate of change of acceleration, Am. J. Phys.46, pp. 1090-1094.
234. Shampine, L. F. and Gordon, M. F. (1975). Computer Solution of Ordinary Differential Equations. The Initial Value Problem(W. H. Freeman, San Francisco).
235. Sharpe, F. R. and Lotka, A. J. (1923). Contribution to the analysis of malaria epidemiology. 4. Incubation lag, Am. J. Hyg.(Supp. 1) 3, pp. 96-112.
236. Shaw, R. (1981). Strange attractors, chaotic behavior, and information flow, Z. Naturforsch.36A, pp. 80-112.
237. Shaw, R. (1984). The Dripping Faucet as a Model Chaotic System(Aerial Press, Santa Cruz, CA).
238. Shimizu, T. and Moroika, N. (1980). On the bifurcation of a symmetric limit cycle to an asymmetric one in a simple model, Phys. Lett. A76, pp. 201-204.
239. Sivashinsky, G. I. (1977). Nonlinear analysis of hydrodynamic instability in laminar flames, Part 1. Derivation of basic equations, Prog. Theor. Phys.63, pp. 1177-1206.
240. Sivashinsky, G. I. and Michelson, D. M. (1980). On the irregular wavy flow of a liquid film flowing down a vertical plane, Prog. Theor. Phys.63, pp. 2112-2117.
241. Smale, S. (1967). Differentiable dynamical systems, Bull. Am. Math. Soc.73, pp. 747-817.
242. Smith, L. A. (2007). Chaos: A Very Short Introduction(Oxford University Press, Oxford).
243. Sompolinsky, H., Crisanti, A., and Sommers, H. J. (1988). Chaos in random neural networks, Phys. Rev. Lett.61, pp. 259-262.
244. Sparrow, C. (1982). The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors(Springer, New York).
245. Sprott, J. C. (1981). Introduction to Modern Electronics(Wiley, New York).
246. Sprott, J. C. (1994). Some simple chaotic flows, Phys. Rev. E50, pp. R647-650.
247. Sprott, J. C. (1997a). Simplest dissipative chaotic flow, Phys. Lett. A228, pp. 271-274.
248. Sprott, J. C. (1997b). Some simple chaotic jerk functions, Am. J. Phys.65, pp. 537-543.
249. Sprott, J. C. (2000a). A new class of chaotic circuit, Phys. Lett. A266, pp. 19-23.
250. Sprott, J. C. (2000b). Simple chaotic systems and circuits, Am. J. Phys.68, pp. 758-763.
251. Sprott, J. C. (2003). Chaos and Time-Series Analysis(Oxford University Press, Oxford).
252. Sprott, J. C. (2005). Dynamical models of happiness, Nonlinear Dynam. Psychol. Life Sci.9, pp. 23-36.
253. Sprott, J. C. (2006). High-dimensional dynamics in the delayed Henon map, Electron. J. Theor. Phys.3, pp. 19-35.
254. Sprott, J. C. (2007a). Maximally complex simple attractors, Chaos 17, pp. 033124-1-6.
255. Sprott, J. C. (2007b). A simple chaotic delay differential equation, Phys. Lett. A 366, pp. 397-402.
256. Sprott, J. C. (2008). Chaotic dynamics on large networks, Chaos 18, pp. 023135-1-9.
257. Sprott, J. C. (2009). Anti-Newtonian dynamics, Am. J. Phys.77, pp. 783-787.
258. Sprott, J. C. and Chlouverakis, K. E. (2007). Labyrinth chaos, Int. J. Bifur. Chaos Appl. Sci. Eng.17, pp. 2097-2108.
259. Sprott, J. C., Vano, J. A., Wildenberg, J. C., Anderson, M. B., and Noel, J. K. (2005a). Coexistence and chaos in complex ecologies, Phys. Lett. A335, pp. 207-212.
260. Sprott, J. C., Wildenberg, J. C., and Vano, J. A. (2005b). A simple spa-tiotemporal chaotic Lotka-Volterra model, Chaos, Solitons Fractals26, pp. 1035-1043.
261. Squire, P. T. (1985). Pendulum damping, Am. J. Phys.54, pp. 984-991.
262. Srzednicki, R. and Wojcik, K. (1997). A geometric method for detecting chaotic dynamics, J. Differ. Equat.135, pp. 66-82.
263. Stewart, I. (2000). Mathematics: The Lorenz attractor exists, Nature 406, pp. 948-949.
264. Storti, D. W. and Rand, R. H. (1982). Dynamics of two strongly coupled van der Pol oscillators, Int. J. Non. Lin. Mech.17, pp. 143-152.
265. Strogatz, S. H. (1994). Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering(Addison-Wesley-Longman, Reading, MA).
266. Strutt, J. W. (1883). On maintained vibrations, Phil. Mag.15, pp. 229-235.
267. Strutt, J. W. (1887). On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with periodic structure, Phil. Mag.24, pp. 145-159.
268. Suarez, M. J. and Schopf, P. S. (1988). A delayed action oscillator for ENSO, J. Atmos. Sci.45, pp. 3283-3287.
269. Sun, K. and Sprott, J. C. (2009). Dynamics of a simplified Lorenz system, Int. J. Bifurcat. Chaos Appl. Sci. Eng.19, pp. 1357-1366.
270. Sussman, G. J. and Wisdom, J. (1992). Chaotic evolution of the Solar System, Science257, pp. 56-62.
271. Tamasevicius, A., Mykolaitis, G., and Bumeliene, S. (2006). Delayed feedback chaotic oscillator with improved spectral characteristics, Electron. Lett.42, pp. 736-737.
272. Tang, K. S., Man, K. F., Zhong, G. Q., and Chen, G. (2001a). Generating chaos via x\x\, IEEE Trans. Circ. Syst.48, pp. 635-641.
273. Tang, W. K. S., Zhong, G. Q., Chen, G., and Man, K. F. (2001b). Generation of N-scroll attractors via sine function, IEEE Trans. Circ. Syst.48, pp. 1369-1372.
274. Tanner, G., Richter, K., and Rost, J. -M. (2000). The theory of two-electron atoms: Between ground state and complete fragmentation, Rev. Mod. Phys. 72, pp. 497-544.
275. Testa, J., Perez, J., and Jeffries, C. (1982). Evidence for universal chaotic behavior of a driven nonlinear oscillator, Phys. Rev. Lett.48, pp. 714-717.
276. Thamilmaran, K., Lakshmanan, M., and Venkatesan, A. (2004). Hyperchaos in a modified canonical Chua’s circuit, Int. J. Bifurcat. Chaos Appl. Sci. Eng. 14, pp. 221-243.
277. Thomas, R. (1999). Deterministic chaos seen in terms of feedback circuits: Analysis, synthesis, ‘labyrnth chaos’, Int. J. Bifurcat. Chaos Appl. Sci. Eng.9, pp. 1889-1905.
278. Thomas, R., Basios, V., Eiswirth, M., Kreul, T., and Rossler, O. E. (2004). Hyperchaos of arbitrary order generated by a single feedback circuit, and the emergence of chaotic walks, Chaos14, pp. 669-674.
279. Torres, L. A. B. and Aguirre, L. A. (2000). Inductorless Chua’s circuit, Electron. Lett.36, pp. 1915-1916.
280. Tsuneda, A. (2005). A gallery of attractors from smooth Chua’s equation, Int. J. Bifurcat. Chaos Appl. Sci. Eng.15, pp. 1-50.
281. Tucker, W. (1999). The Lorenz attractor exists, Compt. Rendus Acad. Sci. Math. 328, pp. 1197-1202.
282. Ueda, Y. (1979). Randomly transitional phenomena in the system governed by Duffing’s equation, J. Stat. Phys.20, pp. 181-196.
283. Ueda, Y. (2001). The Road to Chaos(2nd ed) (A serial Press, Santa Cruz, CA).
284. Vallis, G. K. (1988). Conceptual models of El Nino, J. Geophys. Res.93, pp. 13979-13991.
285. Valtonen, M. and Karttunen, H. (2006). The Three-Body Problem(Cambridge University Press, Cambridge).
286. van Buskirk, R. and Jeffries, C. (1985). Observation of chaotic dynamics of coupled nonlinear oscillators, Phys. Rev. A31, pp. 3332-3357.
287. van der Pol, B. (1920). A theory of the amplitude of free and forced triode vibrations, Radio Review 1, pp. 701-710, 754-762.
288. van der Pol, B. (1926). On relaxation oscillations, Phil. Mag. Ser. 72, pp. 978-992.
289. van der Pol, B. and van der Mark, J. (1927). Frequency demultiplication, Nature 120, pp. 363-364.
290. van der Pol, B. and van der Mark, J. (1928). The heartbeat considered as a relaxation oscillation, and the electrical model of the heart, Phil. Mag. Ser. 76, pp. 763-775.
291. van der Schrier, G. and Maas, L. R. M. (2000). The diffusionless Lorenz equations; Shil’nikov bifurcations and reduction to an explicit map, Phys. Nonlinear Phenom.141, pp. 19-36.
292. Vano, J. A., Wildenberg, J. C., Anderson, M. B., Noel, J. K., and Sprott, J. C. (2006). Chaos in low-dimensional Lokta-Volterra models of competition, Nonlinearity19, pp. 2391-2404.
293. Verhulst, P. F. (1838). Notice sur la loi que la population poursuit dans son accroissement, Correspondance Mathematique et Physique10, pp. 113-121.
294. Villasana, M. and Radunskaya, A. (2003). A delay differential equation model for tumor growth, J. Math. Biol.47, pp. 270-294.
295. Virgin, L. N. (2000). Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration(Cambridge University Press, Cambridge).
296. Virk, G. S. (1985). Runge Kutta method for delay-differential systems, IEE Proc. Contr. Theor. Appl.132, pp. 119-123.
297. Volterra, V. (1926). Variazioni e fluttuazioni del numero d’individui in specie animali conviventi, Memorie dell’ Accademia dei Lincei2, pp. 31-113.
298. Wang, Y., (2009). 3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system, Nonlinear Dynam.56, pp. 453-462.
299. Wang, Y., Singer, J., and Bau, H. H. (1992). Controlling chaos in a thermal convection loop, J. Fluid. Mech.237, pp. 479-498.
300. Wang, X. F., Zhong, G. -Q, Tang, K. -S, Man, K. F., and Liu, Z. -F. (2001). Generating chaos in Chua’s circuit via time-delay feedback, IEEE Trans. Circ. Syst.48, pp. 1151-1156.
301. Wang, G., Zhang, X., Zheng, Y., and Li, Y. (2006). A new modified hyperchaotic Lu system, Phys. Stat. Mech. Appl.371, pp. 260-272.
302. Weinert, K., Webber, O., Husken, M., and Theis, W. (2002). Analysis and prediction of dynamic disturbances of the BTA deep hole drilling process. In Proc. of the 3rd CIRP International Seminar on Intelligent Computation in Manufacturing Engineering, (ed. R. Teti), ICME 2002, Ischia, Italy, pp. 297-302.
303. Weiss, C. O. and Brock, J. (1986). Evidence for Lorenz-type chaos in a laser, Phys. Rev. Lett.57, pp. 2804-2806.
304. Wiggens, S. (1988). Global Bifurcations and Chaos, Analytical Methods(Springer, New York).
305. Wildenberg, J. C., Vano, J. A., and Sprott, J. C. (2005). Complex spatiotemporal dynamics in Lotka-Volterra ring systems, Ecol. Complex.3, pp. 140-147.
306. Woafo, P. and Kadji, H. G. E. (2004). Synchronized states in a ring of mutually coupled self-sustained electrical oscillators, Phys. Rev. E69, pp. 046206-1-9.
307. Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A. (1985). Determining Lyapunov exponents from a time series, Phys. Nonlinear Phenom.16, pp. 285-317.
308. Wright, E. M. (1955). A nonlinear difference-differential equation, J. Reine Angew. Math.194, pp. 66-87.
309. Yalcin, M. E. and Ozoguz, S. (2007). N-scroll chaotic attractors from a first-order time-delay differential equation, Chaos17, pp. 033112-1-8.
310. Yalcin, M. E., Suykens, J. A., and Vandewalle, J. C. L. (2005). Cellular Neural Networks, Multiscroll Chaos and Synchronization(World Scientific, Singapore).
311. Yim, G., Ryu, J., and Park, Y. (2004). Chaotic behaviors of operational amplifiers, Phys. Rev. E69, pp. 045201-1-4.
312. Zabusky, N. J. and Kruskal, M. D. (1965). Interaction of “solitons” in a collisionless plasma and the recurrence of initial states, Phys. Rev. Lett.15, pp. 240-243.
313. Zeghlache, H. and Mandel, P. (1985). Influence of detuning on the properties of laser equations, J. Opt. Soc. Am. B2, pp. 18-22.
314. Zhang, F. and Heidel, J. (1997). Non-chaotic behaviour in three-dimensional quadratic systems, Nonlinearity10, pp. 1289-1303.
315. Zhang, F. and Heidel, J. (1999). Erratum: Non-chaotic behaviour in threedimensional quadratic systems, Nonlinearity12, pp. 739.
316. Zhezherun, A. (2005). Chaotic behavior in piecewise linear Linz-Sprott equations, J. Phys. Conf.22, pp. 235-253.
317. Zhong, G. Q. (1994). Implementation of Chua’s circuit with a cubic nonlinearity, IEEE Trans. Circ. Syst.41, pp. 934-941.
318. Zhou, W., Xu, Y., Lu, H., and Pan, L. (2008). On dynamics analysis of a new chaotic attractor, Phys. Lett. A372, pp. 5773-5777.