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Elegant Chaos : Algebraically Simple Chaotic Flows - Julien Clinton Sprott

Elegant Chaos

Algebraically Simple Chaotic Flows

Hardcover

Published: 30th June 2010
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This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Kossler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos.

No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study.

Prefacep. vii
List of Tablesp. xv
Fundamentalsp. 1
Dynamical Systemsp. 1
State Spacep. 2
Dissipationp. 7
Limit Cyclesp. 8
Chaos and Strange Attractorsp. 10
Poincaré Sections and Fractalsp. 12
Conservative Chaosp. 16
Two-toruses and Quasiperiodicityp. 18
Largest Lyapunov Exponentp. 20
Lyapunov Exponent Spectrump. 24
Attractor Dimensionp. 29
Chaotic Transientsp. 31
Intermittencyp. 32
Basins of Attractionp. 32
Numerical Methodsp. 36
Elegancep. 37
Periodically Forced Systemsp. 41
Van der Pol Oscillatorp. 41
Rayleigh Oscillatorp. 43
Rayleigh Oscillator Variantp. 43
Duffing Oscillatorp. 44
Quadratic Oscillatorsp. 47
Piecewise-linear Oscillatorsp. 48
Signum Oscillatorsp. 49
Exponential Oscillatorsp. 51
Other Undamped Oscillatorsp. 51
Velocity Forced Oscillatorsp. 53
Parametric Oscillatorsp. 55
Complex Oscillatorsp. 57
Autonomous Dissipative Systemsp. 61
Lorenz Systemp. 61
Diffusionless Lorenz Systemp. 64
Rössler Systemp. 66
Other Quadratic Systemsp. 68
Rössler prototype-4 systemp. 68
Sprott systemsp. 68
Jerk Systemsp. 70
Simplest quadratic casep. 73
Rational jerksp. 76
Cubic casesp. 77
Cases with arbitrary powerp. 79
Piecewise-linear casep. 80
Memory oscillatorsp. 82
Circulant Systemsp. 83
Halvorsen's systemp. 84
Thomas' systemsp. 85
Piecewise-linear systemp. 86
Other Systemsp. 86
Multiscroll systemsp. 87
Lotka-Volterra systemsp. 88
Chua's systemsp. 90
Rikitake dynamop. 92
Autonomous Conservative Systemsp. 95
Nosé-Hoover Oscillatorp. 95
Nosé-Hoover Variantsp. 97
Jerk Systemsp. 98
Jerk form of the Nosé-Hoover oscillatorp. 98
Simplest conservative chaotic flowp. 99
Other conservative jerk systemsp. 99
Circulant Systemsp. 101
Quadratic casep. 102
Cubic casep. 102
Labyrinth chaosp. 105
Piecewise-linear systemp. 107
Low-dimensional Systems (D < 3)p. 109
Dixon Systemp. 109
Dixon Variantsp. 110
Logarithmic Casep. 112
Other Casesp. 114
High-dimensional Systems (D > 3)p. 115
Periodically Forced Systemsp. 115
Forced pendulump. 116
Other forced nonlinear oscillatorsp. 118
Master-slave Oscillatorsp. 118
Mutually Coupled Nonlinear Oscillatorsp. 120
Coupled pendulumsp. 121
Coupled van der Pol oscillatorsp. 123
Coupled FitzHugh-Nagumo oscillatorsp. 123
Coupled complex oscillatorsp. 124
Other coupled nonlinear oscillatorsp. 125
Hamiltonian Systemsp. 126
Coupled nonlinear oscillatorsp. 128
Velocity coupled oscillatorsp. 129
Parametrically coupled oscillatorsp. 130
Simplest Hamiltonianp. 130
Hénon-Heiles systemp. 132
Reduced Hénon-Heiles systemp. 133
N-body gravitational systemsp. 134
N-body Coulomb systemsp. 138
Anti-Newtonian Systemsp. 142
Two-body problemp. 142
Three-body problemp. 145
Hyperjerk Systemsp. 147
Forced oscillatorsp. 147
Chlouverakis systemsp. 148
Hyperchaotic Systemsp. 152
Rössler hyperchaosp. 153
Snap hyperchaosp. 154
Coupled chaotic systemsp. 154
Other hyperchaotic systemsp. 156
Autonomous Complex Systemsp. 156
Lotka-Volterra Systemsp. 157
Artificial Neural Networksp. 159
Minimal dissipative artificial neural networkp. 161
Minimal conservative artificial neural networkp. 162
Minimal circulant artificial neural networkp. 162
Circulant Systemsp. 165
Lorenz-Emanuel Systemp. 165
Lotka-Volterra Systemsp. 169
Antisymmetric Quadratic Systemp. 171
Quadratic Ring Systemp. 171
Cubic Ring Systemp. 171
Hyperlabyrinth Systemp. 173
Circulant Neural Networksp. 174
Hyperviscous Ringp. 176
Rings of Oscillatorsp. 176
Coupled pendulumsp. 177
Coupled cubic oscillatorsp. 177
Coupled signum oscillatorsp. 178
Coupled van der Pol oscillatorsp. 179
Coupled FitzHugh-Nagumo oscillatorsp. 180
Coupled complex oscillatorsp. 182
Coupled Lorenz systemsp. 182
Coupled jerk systemsp. 185
Star Systemsp. 185
Coupled pendulumsp. 187
Coupled cubic oscillatorsp. 187
Coupled signum oscillatorsp. 188
Coupled van der Pol oscillatorsp. 190
Coupled FitzHugh-Nagumo oscillatorsp. 191
Coupled complex oscillatorsp. 191
Coupled diffusionless Lorenz systemsp. 193
Coupled jerk systemsp. 194
Spatiotemporal Systemsp. 195
Numerical Methodsp. 195
Kuramoto-Sivashinsky Equationp. 199
Kuramoto-Sivashinsky Variantsp. 200
Cubic casep. 201
Quartic casep. 201
Chaotic Traveling Wavesp. 201
Rotating Kuramoto-Sivashinsky systemp. 203
Rotating Kuramoto-Sivashinsky variantp. 203
Continuum Ring Systemsp. 204
Quadratic ring systemp. 204
Antisymmetric quadratic systemp. 205
Other simple PDEsp. 207
Traveling Wave Variantsp. 212
Time-Delay Systemsp. 221
Delay Differential Equationsp. 221
Mackey-Glass Equationp. 223
Ikeda DDEp. 223
Sinusoidal DDEp. 225
Polynomial DDEp. 225
Sigmoidal DDEp. 227
Signum DDEp. 227
Piecewise-linear DDEsp. 229
Antisymmetric casep. 229
Asymmetric casep. 229
Asymmetric logistic DDEp. 230
Asymmetric Logistic DDE with Continuous Delayp. 232
Chaotic Electrical Circuitsp. 233
Circuit Elegancep. 233
Forced Relaxation Oscillatorp. 234
Autonomous Relaxation Oscillatorp. 237
Coupled Relaxation Oscillatorsp. 239
Two oscillatorsp. 239
Many oscillatorsp. 241
Forced Diode Resonatorp. 242
Saturating Inductor Circuitp. 243
Forced Piecewise-linear Circuitp. 246
Chua's Circuitp. 246
Nishio's Circuitp. 249
Wien-bridge Oscillatorp. 251
Jerk Circuitsp. 254
Absolute-value casep. 254
Single-knee casep. 255
Signum casep. 256
Signum variantp. 258
Master-slave Oscillatorp. 259
Ring of Oscillatorsp. 261
Delay-line Oscillatorp. 263
Bibliographyp. 265
Indexp. 281
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9789812838810
ISBN-10: 9812838813
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 304
Published: 30th June 2010
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 24.13 x 16.51  x 1.91
Weight (kg): 0.59