The nonlinear workbook: Chaos, fractals, cellular automata, genetic algorithms, gene expression programming, support vector machine, wavelets, hidden markov models, fuzzy logic with C++, java and symbolicC++ programs, 5th edition

The Nonlinear Workbook: Chaos, Fractals, Cellular Automata, Genetic Algorithms, Gene Expression Programming, Support Vector Machine, Wavelets, Hidden Markov Models, Fuzzy Logic with C++, Java and SymbolicC++ Programs, 5th Edition

Volumn , Issue , 2011, Pages 1-621

  Steeb, Willi Hans ^a  

^a UNIVERSITY OF JOHANNESBURG   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

C++ (PROGRAMMING LANGUAGE); COMPUTER SOFTWARE; FUZZY LOGIC; GENE EXPRESSION; GENETIC ALGORITHMS; HIDDEN MARKOV MODELS; MATHEMATICAL OPERATORS;

DATA-COMMUNICATION; DIFFERENTIAL FORMS; GENE EXPRESSION PROGRAMMING; T - NORM; T-CONORMS; THEORETICAL ASPECTS; WORKED-OUT EXAMPLES;

JAVA PROGRAMMING LANGUAGE;

EID: 84995446632     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/8050     Document Type: Book

References (230)

1. Abraham R. and Marsden J. E., Foundations of Mechanics, second edition, Benjamin/Cummings, 1982
2. Ahuja R. K., Magnanti T. L. and Orlin J. B., Network Flows, Prentice Hall, 1993
3. Antoine J.-P., Murenzi R., Vandergheynest P. and Ali S. T., Two-dimensional wavelets and their relatives, Cambridge University Press, 2004
4. Arbib M. A. (Editor), The Handbook of Brain Theory and Neural Networks, second edition, MIT Press, 2003
5. Arnold V. I., Mathematical Methods of Classical Mechanics, Springer, 1979
6. Arnold V. I. and Avez A., Ergodic Problems of Classical Mechanics, Addison-Wesley, 1989
7. Arrowsmith D. K. and Place C. M., An Introduction to Dynamical Systems, Cambridge University Press, 1990
8. Bac Fam Quang and Perov V. L., New evolutionary genetic algorithms for NP-complete combinatorial problems, Biological Cybernetics 69, 229-234, 1993
9. Babuska R., Fuzzy Modeling for Control, Kluwer, 1998
10. Baker G. L. and Gollub J., Chaotic Dynamics: An Introduction, Cambridge University Press, 1990
11. Bandemer H. and Gottwald S., Fuzzy Sets, Fuzzy Logic, Fuzzy Methods with Applications, John Wiley, 1995
12. Barnsley M., Fractals Everywhere, Academic Press, 1988
13. Barnsley M., Fractals Everywhere, Morgan Kaufmann, 2000
14. Bauer M. and Martienssen W., Lyapunov exponents and dimensions of chaotic neural networks, J. Phys. A: Math. Gen. 24, 4557-4566, 1991
15. Bazaraa M. S. and Shetty C. M., Nonlinear Programming, Wiley, 1979
16. Beardon A. F., Iteration of Rational Functions, Springer, 1991
17. Becchetti C. and Ricotti L. P., Speech Recognition: Theory and C++ Implementation, Wiley, 2002
18. Bellman R., The stability of solutions of linear differential equations, Duke Math. J. 10, 643-647, 1943
19. Bellman R Wavelets: Mathematics and Applications, Edited by John J. Benedetto and Michael W. Frazier, CRC Press, 1994
20. Bojadziev G. and Bojadziev M., Fuzzy Sets, Fuzzy Logic, Applications, World Scientific, Singapore, 1995
21. Bookstein A., Klein S. T. and Raita T. Fuzzy Hamming distance in Combinatorial pattern machting, Springer, 2006
22. Bowen R., Methods of Symbolic Dynamics, Springer, 1975
23. Broomhead D. S., Huke J. P. and Muldoon M. R., Linear filters and nonlinear systems, J. Roy. Stat. Soc. B 54, 373-382, 1992
24. Brown R. and Kocarev L., A unifying definition of synchronization for dynamical systems, Chaos 10, 344-349, 2000
25. Buhmann M. D., Radial Basis Functions: Theory and Implementations, Cambridge University Press, 2003
26. Cartan H., Differential Forms, Dover Books on Mathematics, 1950
27. Chaitin G. J., Information, Randomness and Incompleteness, World Scientific, Singapore, 1987
28. Charniak E., Statistical Language Learning, MIT Press, 1993
29. Chechkin A., Gonchar V., Klafter J. and Metzler, Fundamentals of Levy Flight Processes, Adv. Chem. Phys. 133B, 439-451, 2006
30. Chen G. and Dong X., On Feedback Control of Chaotic Continuous-Time Systems, IEEE Trans. Circuits Syst. 40, 591-601, 1993
31. Chen L. and Aihara K., Chaotic simulated annealing by a neural network model with transient chaos, Neural Networks 8, 915-930, 1995
32. Cherbit G. (editor), Fractals: Non-integral dimensions and applications, Wiley, 1991
33. Chow S. N. and Hale J. K., Methods of Bifurcation Theory, Springer, 1982
34. Chui C. K., An Introduction to Wavelets, Academic Press, 1992
35. Cichocki A. and Unbehauen R., Neural Networks for Optimization and Signal Processing, Wiley, 1993
36. Cohen A., Daubechies I. and Feauveau J.-C., Biorthogonal bases of compactly supported wavelets, Comm. Pure and Appl. Math. 45, 485-560, 1992
37. Collet P. and Eckmann J. P., Iterated Maps on the interval as Dynamical Systems, Birkhauser, Boston, 1980
38. Collins J. J. and Stewart I., Hexapodal gaits and coupled nonlinear oscillators models, Biol. Cybern. 68, 287-298, 1993
39. Collins J. J. and Richmond S. A., Hard-wired central pattern generators for quadrupedal locomotion, Biol. Cybern. 71, 375-385, 1994
40. Contopolous G., Galgani L. and Giorgilli A., On the Number of Isolating Integrals in Hamiltonian Systems, Phys. Rev. A, 18, 1183-1190, 1978
41. Cristianni N. and Hahn M. W., Introduction to Computational Genomics, Cambridge University Press, 2007
42. Cronje G. A. and Steeb W.-H., Genetic Algorithms in a Distributed Computing Enviroment Using PVM, International Journal of Modern Physics C 8, 327-344, 1997
43. Cybenko G., Approximation by superpositions of a sigmoidal function, Mathematics of Control, Signals and Systems 2, 303-314, 1989
44. Daubechies I., Ten Lectures on Wavelets, SIAM, 1992
45. Davis H. T., Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, 1962
46. Deslauriers G., Dubuc S. and Lemire D., Une famille d’ondelettes biorthogo-nales sur l’intervalle obtenue par un schema d’ interpolation iterative, Ann. Sci. Math. Quebec 23, 37-48, 1999
47. Devaney R. L., An Introduction to Chaotic Dynamical Systems, Second Edition, Addison-Wesley, 1989
48. Doob J. L., Stochastic Processes, Wiley, 1953
49. Dorbec P. and Gajardo A., Lanton’s fly, J. Phys. A: Math. Theor. 41, 405-101, 2008
50. Dubois D. and Prade H., Fuzzy Sets and Systems: Theory and Applications, Academic Press, 1980
51. Eckmann J.-P. and Ruelle D., Ergodic Theory of Chaos and Strange Attractors, Reviews of Modern Physics 57, 617-655, 1985
52. Eckmann J.-P., Kamphorst S. O., Ruelle D. and Ciliberto S., Liapunov Exponents from Time Series, Physical Review A 34, 4971-4979, 1986
53. Edgar G. A., Measure, Topology, and Fractal Geometry, Springer, 1990
54. Elizondo D. A., Birkenhead R., Gongora M., Taillard E. and Luyima P., Analysis and test of efficient methods for building recursive deterministic perceptron neural networks, Neural Networks 20, 1095-1108, 2007
55. Elizondo D. A., Birkenhead R., Gongora M., Taillard E. and Luyima P.Wavelets: Theory and Applications, Edited by Gordon Erlebacher, M. Pousuff Hussaini, Leland M. Jameson, Oxford University Press, 1996
56. Falconer K. J., The Geometry of Fractal Sets, Cambridge University Press, 1985
57. Fausett L., Fundamentals of Neural Networks: Architecture, Algorithms and Applications, Prentice Hall, 1994
58. Ferreira C., Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence, 2nd edition, Springer, 2006
59. Ferreira C., Gene Expression Programming: A New Adaptive Algorithm for Solving Problems, http://xxx.lanl.gov, cs.AI/0102027
60. Fisher R. A., The use of multiple measurements in taxonomic problems, Annals of Eugenics 7, 179-188, 1936
61. Flanders H., Differential Forms with Applications to the Physical Sciences, Academic Press, 1963
62. Frisch U., Hasslacher B. and Pommeau Y., Lattice gas methods for partial differential equations, Phys. Rev. Lett. 56, 1505-1508, 1986
63. Friefi T.-T., Christianni N. and Campbell C., The Kernel-Adatron Algorithm: A fast and simple learning procedure for support vector machines, Proceedings of the 15th International Conference on Machine Learning, pp. 188-196, Morgan Kaufmann, 1998
64. Froberg C. E., Numerical Mathematics: Theory and Computer Applications, Benjamin-Cummings, 1985
65. Funahashi K.-I., On the approximate realization of continuous mappings by neural networks, Neural Networks 2, 183-192, 1989
66. Gajardo A., Moreira A. and Goles E., Complexity of Langton’s ant, Discrete Appl. Maths. 117, 41-50, 2002
67. Gao T., Chen Z., Yuan Z. and Chen G., A hyperchaos generated from Chen’s system, Int. J. Mod. Phys. C 17, 471-478, 2006
68. Gardner M., Mathematical Games: The fanatastic combinations of John Conway’s new solitaire game’Life’, Scientific American 223, 120-123, 1970
69. Goldberg D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, 1989
70. Goldberg D. E. and Lingle R., Alleles, Loci, and the TSP, in Greffenstette, J. J. (Editor), Proceedings of the First International Conference on Genetic Algorithms, Lawrence Erlbaum Associates, Hillsdale, NJ, 1985
71. Gonzalez-Miranda J.M., Synchronization and Control of Chaos, Imperial College Press, 2004
72. Grassberger P. and Procaccia I., Characterization of strange attractors, Physical Review Letters 50, 346-349, 1983
73. Grobner W. (editor), Contributions to the method of Lie series, Bibliographis-ches Institut, Mannheim, 1967
74. Gronwall T. H., Note on the derivative with respect to a parameter of the solutions of a system of differential equations, Ann. of Math. 20, 292-296, 1919
75. Guckenheimer J. and Holmes P., Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer, 1983
76. Guillemin V. and Sternberg S., Symplectic Techniques in Physics, Cambridge University Press, 1984
77. Gumowski I. and Mira C., Recurrences and Discrete Dynamical Systems, Springer, 1980
78. Gusfield D., Algorithms on strings, trees and sequences: computer science and computational biology, Cambridge University Press, 1997
79. Hairer E., Norsett S. P. and Wanner G., Solving Ordinary Differential Equations I, 2nd revised edition, Springer, 1993
80. Hajek P., Metamathematics of Fuzzy Logic, Kluwer, 1998
81. Hao Bai-Lin, Elementary Symbolic Dynamics and Chaos in Dissipative Systems, World Scientific, Singapore, 1989
82. Hao Bai-Lin, Symbolic Dynamics and Characterization of Complexity, Physica D 51, 161-176, 1991
83. Hardy Y., Steeb W.-H. and Villet C. M., Stabilization of Chaotic Systems with Phase Coupling, Z. Naturf. 55a, 847-850, 2000
84. Hardy Y. and Steeb W.-H., Classical and Quantum Computing with C++ and Java Simulations, Birkhauser Verlag, Basel, 2001
85. Hardy Y., Steeb W.-H. and Stoop R., Genetic algorithms, floating point numbers and applications, Int. J. of Modern Physics C 16, 1801-1804, 2005
86. Hardy Y. and Sabatta D., Encoding, symbolic dynamics, cryptography and C++ implementations, Phys. Lett. A 366, 575-584, 2007
87. Hardy Y., Kiat Shi Tan and Steeb W.-H., Computer Algebra with Symbol-icC++, World Scientific, Singapore, 2008
88. Hardy A. and Steeb W.-H., Mathematical Tools in Computer Graphics with C# Implementations, World Scientific, Singapore, 2007
89. Hassoun M. H., Fundamentals of Artificial Neural Networks, The MIT Press, 1995
90. Haykin S., Neural Networks, Macmillan College Publishing Company, 1994
91. Hebb D., The organization of behaviour, Wiley, 1949
92. Hedlund G. A., Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory 3, 320-371, 1969
93. Hernandez E. and Weiss G., A First Course on Wavelets, CRC Press, 1996
94. Herz A., Sulzer B., Kuhn R. and van Hemmen J., The Hebb rule: storing static and dynamic objects in an associative neural network, Europhysics Letters 7, 663-669, 1988
95. Higuchi T., Approach to an irregular time series on the basis of fractal theory, Physica D 31, 277-283, 1988
96. Hirsch M. W. and Smale S., Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, 1974
97. Holland J. H., Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, 1975
98. Holmgren R. A., A First Course in Discrete Dynamical Systems, Springer, 1994
99. Hopfield J. J., Neural networks and physical systems with emergent collective computational abilities, Proceedings of the National Academy of Sciences of the USA 79, 2554-2558, 1982
100. Hornik K., Stinchcombe M. and White H., Multilayer feedforward networks are universal approximators, Neural Networks 2, 359-366, 1989
101. Hiibler A. W., Adaptive Control of Chaotic Systems, Helvetica Physica Acta 62, 343-346, 1989
102. Hurst H. E., Long Term Storage Capacity of Reservoirs, Trans. Am. Soc. Civil Eng. 116, 770-776, 1951
103. Iooss G. and Joseph D. D., Elementary Stability and Bifurcation Theory, second edition, Springer, 1990
104. Jelinek F., Statistical Methods for Speech Recognition, The MIT Press, 1997
105. Jensen A. and La Cour-Harbo A., Ripples in mathematics: The discrete wavelet transform, Springer, 2001
106. Jordan D. W. and Smith P., Nonlinear Ordinary Differential Equations, Clarendon Press, Oxford, 1985
107. Julia G. M., Memoire sur literation des fonctions rationnelles, Journal de Mathematiques Pures et Appliquees 8, 47-245, 1918
108. Kahan W., IEEE Standard 754 for binary floating-point arithmetic, Lectures Notes on the Status of IEEE 754, Work in Progress, 1996
109. Kamp Y. and Hasler M., Recursive Neural Networks for Associative Memory, Wiley, 1990
110. Kaneko K. and Konishi T., Diffusion in Hamiltonian dynamical systems with many degrees of freedom, Phys. Rev. A 40, 6130-6133, 1989
111. Kantz H., A robust method to estimate the maximal Lyapunov exponent of a time series, Physics Letters A 185, 77-87, 1994
112. Kapitaniak T., Controlling Chaos, Harcourt Brace, 1996
113. Kawakami H., Bifurcation of Periodic Responses in Forced Dynamics, IEEE Trans. Circuits Syst. CAS-31, 248-256, 1984
114. Klement E. P., Mesiar R. and Pap E., Triangular norms, Kluwer, 2000
115. Kluiving R., Capel H. W. and Pasmanter R. A., Phase-Transition Like Phenomenon in a Piecewise Linear Map, Physica A 164, 593-624, 1990
116. Knapp H. and Wanner G., On the numerical treatment of ordinary differential equations, Contributions to the Method of Lie series, Chapter II, pp. 43-97, Bibliographisches Institut, Mannheim, 1967
117. Koch H. von, Sur une courbe continue sans tangente, obtenue par une construction geometrique elementair, Archiv for Matemat. Astron. och Fys. 1, 681702, 1904
118. Kohonen T., Self-Organization and Associative Memory, third edition, Springer, 1989
119. Kohonen T., Self-Organizing Maps, third edition, Springer, 2001
120. Koski T., Hidden Markov Models for Bioinformatics, Springer, 2001
121. Kowalski K. and Steeb W.-H., Nonlinear Dynamical Systems and Carleman Linearization, World Scientific, Singapore, 1991
122. Kuhn H. W. and Tucker A. W., Nonlinear Programming, Proceedings of the 2nd Berkeley Symposium, Berkeley: University of California Press, 481-492, 1951
123. Kuznetsov Y. A., Elements of Applied Bifurcation Theory, second edition, Springer, 1998
124. Lai Y.-C., Encoding Digital Information using Transient Chaos, Int. J. Bifur. Chaos 10, 787-795, 2000
125. Lai Y.-C. and Grebogi C., Synchronization of chaotic trajectories using control, Phys. Rev. 47, 2357-2362, 1993
126. Langton C. G., Studying artificial life with cellular automata, Physica D 22, 120-149, 1986
127. Lempel A. and Ziv J., On the Complexity of Finite Sequences, IEEE Transactions on Information Theory IT-22, 75-81, 1976
128. Lichtenberg A. J. and Lieberman M. A., Regular and Stochastic Motion, Springer, 1983
129. Lin J.-S., Cheng K.-S. and Mao C.-W., Segmentation of Multispectral Magnetic Resonance Image Using Penalized Fuzzy Competitive Learning Network, Computers and Biomedical Research 29, 314-326, 1996
130. Lindenmayer A., Mathematical models for cellular interaction in development, J. Theoret. Biology 18, 280-315, 1968
131. Liu Y., You Z. Cao L., A functional neural network computing some eigenvalues and eigenvectors of a special real matrix, Neural Networks 18, 1293-1300, 2005
132. Lorenz E. N., Deterministic Non-Periodic Flow, J. Atmos. Sci. 20, 130-141, 1963
133. Lopez-Ruiz R. and Perez-Garcia C., Dynamics of maps with a global multi-plicate coupling, Chaos, Solitons and Fractals 1, 511-528, 1991
134. Lopez-Ruiz R. and Perez-Garcia C., Dynamics of two logistic maps with a multiplicate coupling, Int. J. of Bifurcation and Chaos 2, 421-425, 1992
135. Luo Fa-Long and Unbehauen R., Applied Neural Networks for Signal Processing, Cambridge University Press, 1997
136. MacKay R. S. and Meiss J. D. (Editors), Hamiltonian Dynamical Systems, Adam Hilger, Bristol, 1987
137. Mandelbrot B. B. and Wallis J. R., Noah, Joseph and operational hydrology, Water Resources Research 4, 909-918, 1968
138. Mandelbrot B. B. and Van Ness J. W., Fractional Brownian motions, fractional noises and applications, SIAM Review 10, 422-437, 1968
139. Mandelbrot B. B., The Fractal Geometry of Nature, Freeman, New York, 1982
140. Maniezzo V., Genetic Evolution of the Topology and Weight Distribution of Neural Networks, IEEE Transactions of Neural Networks 5, 39-53, 1994
141. Marek M. and Schreiber I., Chaotic behaviour of deterministic dissipative systems, Cambridge University Press, 1991
142. Marsden J. E. and McCracken M., The Hopf Bifurcation and its Applications, Springer, 1976
143. Matsumoto T., Chua L. O. and Kobayashi K., Hyperchaos: Laboratory Experiment and Numerical Confirmation, IEEE Trans. Circuits Syst. vol. CAS-33, 1143-1147, 1986
144. McLaren D. I. and Quispel G. R. W., Integral-preserving integrators, J. Phys. A: Math. Gen. 37, L489-L495, 2004
145. Michalewicz Z., Genetic Algorithms + Data Structure = Evolution Programs, Third Edition, Springer, 1996
146. Mika S., Ratsch G., Weston J., Scholkopf B. and Muller K.-R., Fisher discriminant analysis with kernels. In Neural Networks for Signal Processing: Vol. IX, 41-48, New York: IEEE Press, 1999
147. Mika S., Ratsch G., Weston J., Scholkopf B., Smola A. J. and Muller K.-R., Invariance features extraction and classification in feature space. In S. A. Solla, T. K. Keen and K.-R. Muller (editors) Advances in neural information processing systems: Vol. 12, pp. 526-532, MIT Press, 2000
148. Minskey M. L. and Papert S. A., Perceptrons, MIT Press, 1969
149. Mira C., Chaotic Dynamics: From the One-dimensional Endomorphism to the Two-dimensional Diffeomorphism, World Scientific, Singapore, 1987
150. Mitchell M., An Introduction to Genetic Algorithms, MIT Press, 1966
151. Mosekilde E., Maistrenko Y. and Postnov D., Chaotic Synchronization, World Scientific, Singapore 2002
152. Munkres J., Topology, 2nd edition, Prentice Hall, 1999
153. m, m 3, Communications in Mathematical Physics 64, 35-40, 1979
154. Oltean M., “Multi Expression Programming”, Technical Report, Babes-Bolyai University, Romania
155. Oltean M., Evolving Evolutionary Algorithms with Patterns, Soft Computing 11, 503-518, 2007
156. Ott E., Grebogi C. and Yorke J. A., Controlling Chaos, University of Maryland, Laboratory for Plasma Research, 1989
157. Ott E., Grebogi C. and Yorke J. A., Controlling Chaos, Phys. Rev. Lett. 64, 1196-1199, 1990
158. Parlitz U. and Lauterborn W., Resonances and Torsion Numbers of Driven Dissipative Nonlinear Oscillators, Z. Naturforsch. 41a, 606-614, 1986
159. Parlitz U. and Lauterborn W., Period-doubling cascades and devil’s staircases of a driven van der Pol oscillators, Phys. Rev. A 36, 1428-1436, 1987
160. Pecora L. M. and Carroll T. L., Synchronization in Chaotic Systems, Phys. Rev. Lett. 64, 821-824, 1990
161. Pedrycz W. and Succi G., fXOR fuzzy logic networks, Soft Computing 7, 115-120, 2002
162. Peitgen H.-O. and Richter P. H., The Beauty of Fractals, Springer, 1986
163. Peitgen H.-O., Jurgens H. and Saupe D., Chaos and Fractals: new frontiers in science, 2nd edition, Springer, 2004
164. Penna T. J., A bit-string model for biological aging, J. Stat. Phys. 78, 1629, 1995
165. Peters E., Fractal Market Analysis: Applying Chaos Theory to Investment and Economics, Wiley, 1994
166. Pikovsky A., Rosenblum M. and Kurths J., Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University Press, 2001
167. Polymilis C., Servizi G., Skokos Ch., Turchetti T. and Vrahatis M. N., Locating periodic orbits by topological degree theory, arXiv:nlln 0211044v1
168. Protter M. H., Basic elements of real analysis, Springer, 1998
169. Pyragas K., Continuous Control by Self-Controlling Feedback, Phys. Lett. A 170, 421-428, 1992
170. Pyragas K., Control of Chaos via Unstable Delayed Feedback-Controller, Phys. Rev. Lett. 86, 2265-2268, 2001
171. Rabiner L., A tutorial on Hidden Markov Models and selected applications in speech recognition, Proceedings of the IEEE 77, 257-286, 1989
172. Rabiner L. and Juang B.-H., Fundamentals of Speech Recognition, Prentice Hall, 1993
173. Rojas R., Neural Networks, Springer, 1996
174. Rosenstein M. T., Collins J. J. and De Luca C. J., A practial method for calculating largest Lyapunov exponents from small data sets, Physica D 65, 117-134, 1993
175. Ross T. J., Fuzzy Logic with Engineering Applications, McGraw-Hill, New York, 1995
176. Rossler O. E., An equation for hyperchaos, Phys. Letters A 71, 155-158, 1979
177. Ruelle D., Chaotic Evolution and Strange Attractors, Cambridge University Press, 1989
178. Saadi K., Talbot N. L. C. and Cawley G. C., Optimally regularised kernel Fisher discriminant classification, Neural Networks 20, 832-841, 2007
179. Sano M. and Sawada Y., Measurement of the Lyapunov Spectrum from Chaotic Time Series, Phys. Rev. Lett. 55, 1082-1085, 1985
180. Sasao T., Logic Synthesis and Optimization, Kluwer, 1993
181. Sato S., Sano M. and Sawada Y., Practical methods of measuring the generalized dimension and the largest Lyapunov exponent in high dimensional chaotic systems, Progess in Theoretical Physics 77, 1-5, 1987
182. Scheid F,. Numerical Analysis, Schaum’s Outline Series, McGraw Hill, 1968
183. Scholl E. and Schuster H. G. (Editors), Handbook of Chaos Control, Wiley-VCH, second edition, 2008
184. Schuster H. G., Martin S. and Martienssen W., New Method for Determing the Largest Liapunov Exponent of Simple Nonlinear Systems, Phys. Rev. A 33, 3547-3549, 1986
185. Seydel R., From Equilibrium to Chaos, Elsevier, New York, 1988
186. Shlesinger M. G., Zaslavsky G. M. and Klafter J., Strange kinetics, Nature 363, 31-37, 1993
187. Sparrow C., The Lorenz Equations: Bifurcations, Chaos and Strange Attractors, Springer, 1982
188. Smale S., On the mathematical foundations of electrical circuits theory, J. Differential Geometry 7, 193-210, 1972
189. Steeb W.-H., A Handbook of Terms Used in Chaos and Quantum Chaos, Bib-liographisches Institut, Mannheim, 1991
190. Steeb W.-H., Chaos und Quantenchaos in Dynamischen Systemen, Bibli-ographisches Institut, Mannheim, 1994
191. Steeb W.-H. and Louw J., Chaos and Quantum Chaos, World Scientific, Singapore, 1986
192. Steeb W.-H., Louw J. A. and Villet C. M., Chaos in Yang-Mills equations, Phys. Rev. D 33, 1174-1176, 1986
193. Steeb W.-H., Solms F., Tan Kiat Shi, and Stoop R., Cubic Map, Complexity and Ljapunov Exponent, Physica Scripta 55, 520-522, 1997
194. Steeb W.-H., Matrix Calculus and Kronecker Product with Applications and C++ Programs, World Scientfic, Singapore, 1997
195. Steeb W.-H., Hardy Y., Hardy A., and Stoop R., Problems and Solutions in Scientific Computing with C++ and Java Simulations, World Scientific, Singapore 2004
196. Steeb W.-H. and Andrieu E. C., Ljapunov Exponents, Hyperchaos and Hurst Exponent, Z. Naturf. 60a, 252-254, 2005
197. Steeb W.-H., Problems and Solutions in Introductory and Adanced Matrix Calculus, World Scientific, Singapore 2006
198. Steeb W.-H., Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra, second edition, World Scientific, Singapore 2007
199. Steeb W.-H. and Hardy Y., A Chaotic Map and Data Transmission, Z. Naturf. 65a, 613-614, 2010
200. Stoop R. and Meier P.F., Evalution of Lyapunov exponents and scaling functions from time series, J. Opt. Soc. Am. B 5, 1037-1045, 1988
201. Suhchik M., Tsimring L. S. and Volkovskii, Performance Analysis of Correlation-based Communication Schemes utilizing Chaos, IEEE Trans. Circuits 147, 1684-1691, 2000
202. Sznajd-Weron K. and Sznajd J., Opinion Evolution in Closed Comminity, Int. J. Mod. C 11, 1157-1165, 2000
203. Tan Z., Hepburn B. S., Tucker C. and Ali M. K., Pattern Recognition Using Chaotic Neural Networks, Discrete Dynamics in Nature and Society 2, 243-247, 1998
204. Toda M., Theory of Nonlinear Lattices, second edition, Springer, 1988
205. Trotter H. F., On the product of semi-groups of operators, Proceedings of the American Mathematical Society 10, 545-551, 1959
206. Ueda Y., Akamatsu N. and Hayashi C., Computer Simulations and NonPeriodic Oscillations, Trans. IEICE Japan 56A, 218-225, 1973
207. Ueda Y. and Akamatsu N., Chaotically Transitional Phenomena in the Forced Negative-Restistance Oscillator, IEEE Trans. Circuits Syst. CAS-28, 217-224, 1981
208. Uezu T., Topology in Dynamical Systems, Phys. Lett. 93A, 161-166, 1983
209. Van Wyk A. and Steeb W.-H., Chaos in Electronics, Kluwer, 1997
210. Vapnik V., Statistical Learning Theory, Wiley, 1998
211. Vapnik V., The nature of statistical learning theory, second edition, Springer, 2000
212. Verlet L., Computer Experiments on Classical Fluids I. Thermodynamical Properties of Lennard-Jones Molecules, Phys. Rev. 159, 98-104, 1967
213. von Westenholz C., Differential Forms in Mathematical Physics, North-Holland, 1978
214. Wang C. and Ge S. S., Adaptive synchronization of uncertain chaotic systems via backstepping design, Chaos, Solitons and Fractals 12, 1199-1206, 2001
215. Wang L. (editor), Support vector machine: theory and applications, Springer, 2005
216. Walters P., An Introduction to Ergodic Theory, Springer, 1982
217. Wolf A., Swift J. B., Swinney H.L., and Vastano J. A., Determining Lyapunov Exponents From Time Series, Physica D 16, 258-317, 1985
218. Wolfram S., Theory and Applications of Cellular Automata, World Scientific, Singapore, 1986
219. Wolfram S., A New Kind of Science, Champaign, IL., Wolfram Media, 2002
220. Xiang-Jun W., Jing-Sen L. and Guan-Rong C., Chaos synchronization of Rik-itake chaotic attractor using the passive control technique, Nonlinear Dynamics 53, 45-53, 2007
221. Yager R. R. and Zadeh L. A. (Editors), Fuzzy Sets, Neural Networks, and Soft Computing, Van Nostrand Reinhold, New York, 1994
222. Yamaguchi Y., Tanikawa K. and Mishima N., Fractal basin boundary in dynamical systems and the Weierstrass-Takagi functions, Phys. Lett. A 128, 470478, 1988
223. Yamamoto T. and Kaneko K., Helium atom as a Classical Three-Body Problem, Phys. Rev. Lett. 70, 1928-1930, 1993
224. Yoshida H., Construction of higher order symplectic integrators, Physics Letters A 150, 262-268, 1990
225. Young L.-S., Dimension, entropy and Lyapunov exponents, Ergodic Theory and Dynamical Systems 2, 109-124, 1982
226. Zaslavskii G. M., Sagdeev R.Z., Chaikovskiii D. K. and Chernikov A. A., Chaos and two-dimensional random walk in periodic and quasiperiodic fields, Zh. Eksp. Teor. Fiz. 97, 1723-1733, 1989
227. Zhang H., Liu D. and Wang Z., Controlling Chaos: Suppression, Synchronization and Chaotification, Springer, 2009
228. Zhang J. and Knoll A., Constructing Fuzzy Controlles with B-Spline Methods - Principles and Applications, International Journal of Intelligent Systems 13, 257-286, 1998
229. Zimmermann H.-J., Fuzzy Set Theory and its Applications, second edition, Kluwer, 1994
230. Zizza F., Differential Forms for Constrained Max-Min Problems: Eliminating Lagrange Multipliers, The College Mathematical Journal 29, 387-396, 1998