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E-raamat: Elegant Chaos: Algebraically Simple Chaotic Flows

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(Univ Of Wisconsin-madison, Usa)
  • Formaat: 304 pages
  • Ilmumisaeg: 22-Mar-2010
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814468671
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Elegant Chaos: Algebraically Simple Chaotic FlowsSuurem pilt
  • Formaat: 304 pages
  • Ilmumisaeg: 22-Mar-2010
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814468671
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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.

Preface vii
List of Tables
xv
1 Fundamentals
1(40)
1.1 Dynamical Systems
1(1)
1.2 State Space
2(5)
1.3 Dissipation
7(1)
1.4 Limit Cycles
8(2)
1.5 Chaos and Strange Attractors
10(2)
1.6 Poincare Sections and Fractals
12(4)
1.7 Conservative Chaos
16(2)
1.8 Two-toruses and Quasiperiodicity
18(2)
1.9 Largest Lyapunov Exponent
20(4)
1.10 Lyapunov Exponent Spectrum
24(5)
1.11 Attractor Dimension
29(2)
1.12 Chaotic Transients
31(1)
1.13 Intermittency
32(1)
1.14 Basins of Attraction
32(4)
1.15 Numerical Methods
36(1)
1.16 Elegance
37(4)
2 Periodically Forced Systems
41(20)
2.1 Van der Pol Oscillator
41(2)
2.2 Rayleigh Oscillator
43(1)
2.3 Rayleigh Oscillator Variant
43(1)
2.4 Duffing Oscillator
44(3)
2.5 Quadratic Oscillators
47(1)
2.6 Piecewise-linear Oscillators
48(1)
2.7 Signum Oscillators
49(2)
2.8 Exponential Oscillators
51(1)
2.9 Other Undamped Oscillators
51(2)
2.10 Velocity Forced Oscillators
53(2)
2.11 Parametric Oscillators
55(2)
2.12 Complex Oscillators
57(4)
3 Autonomous Dissipative Systems
61(34)
3.1 Lorenz System
61(3)
3.2 Diffusionless Lorenz System
64(2)
3.3 Rossler System
66(2)
3.4 Other Quadratic Systems
68(2)
3.4.1 Rossler prototype-4 system
68(1)
3.4.2 Sprott systems
68(2)
3.5 Jerk Systems
70(13)
3.5.1 Simplest quadratic case
73(3)
3.5.2 Rational jerks
76(1)
3.5.3 Cubic cases
77(2)
3.5.4 Cases with arbitrary power
79(1)
3.5.5 Piecewise-linear case
80(2)
3.5.6 Memory oscillators
82(1)
3.6 Circulant Systems
83(3)
3.6.1 Halvorsen's system
84(1)
3.6.2 Thomas' systems
85(1)
3.6.3 Piecewise-linear system
86(1)
3.7 Other Systems
86(9)
3.7.1 Multiscroll systems
87(1)
3.7.2 Lotka-Volterra systems
88(2)
3.7.3 Chua's systems
90(2)
3.7.4 Rikitake dynamo
92(3)
4 Autonomous Conservative Systems
95(14)
4.1 Nose-Hoover Oscillator
95(2)
4.2 Nose-Hoover Variants
97(1)
4.3 Jerk Systems
98(3)
4.3.1 Jerk form of the Nose-Hoover oscillator
98(1)
4.3.2 Simplest conservative chaotic flow
99(1)
4.3.3 Other conservative jerk systems
99(2)
4.4 Circulant Systems
101(8)
4.4.1 Quadratic case
102(1)
4.4.2 Cubic case
102(3)
4.4.3 Labyrinth chaos
105(2)
4.4.4 Piecewise-linear system
107(2)
5 Low-dimensional Systems (D > 3)
109(6)
5.1 Dixon System
109(1)
5.2 Dixon Variants
110(2)
5.3 Logarithmic Case
112(2)
5.4 Other Cases
114(1)
6 High-dimensional Systems (D > 3)
115(50)
6.1 Periodically Forced Systems
115(3)
6.1.1 Forced pendulum
116(2)
6.1.2 Other forced nonlinear oscillators
118(1)
6.2 Master-slave Oscillators
118(2)
6.3 Mutually Coupled Nonlinear Oscillators
120(6)
6.3.1 Coupled pendulums
121(2)
6.3.2 Coupled van der Pol oscillators
123(1)
6.3.3 Coupled FitzHugh-Nagumo oscillators
123(1)
6.3.4 Coupled complex oscillators
124(1)
6.3.5 Other coupled nonlinear oscillators
125(1)
6.4 Hamiltonian Systems
126(16)
6.4.1 Coupled nonlinear oscillators
128(1)
6.4.2 Velocity coupled oscillators
129(1)
6.4.3 Parametrically coupled oscillators
130(1)
6.4.4 Simplest Hamiltonian
130(2)
6.4.5 Henon-Heiles system
132(1)
6.4.6 Reduced Henon-Heiles system
133(1)
6.4.7 iV-body gravitational systems
134(4)
6.4.8 iV-body Coulomb systems
138(4)
6.5 Anti-Newtonian Systems
142(5)
6.5.1 Two-body problem
142(3)
6.5.2 Three-body problem
145(2)
6.6 Hyperjerk Systems
147(5)
6.6.1 Forced oscillators
147(1)
6.6.2 Chlouverakis systems
148(4)
6.7 Hyperchaotic Systems
152(4)
6.7.1 Rossler hyperchaos
153(1)
6.7.2 Snap hyperchaos
154(1)
6.7.3 Coupled chaotic systems
154(2)
6.7.4 Other hyperchaotic systems
156(1)
6.8 Autonomous Complex Systems
156(1)
6.9 Lotka-Volterra Systems
157(2)
6.10 Artificial Neural Networks
159(6)
6.10.1 Minimal dissipative artificial neural network
161(1)
6.10.2 Minimal conservative artificial neural network
162(1)
6.10.3 Minimal circulant artificial neural network
162(3)
7 Circulant Systems
165(30)
7.1 Lorenz-Emanuel System
165(4)
7.2 Lotka-Volterra Systems
169(2)
7.3 Antisymmetric Quadratic System
171(1)
7.4 Quadratic Ring System
171(1)
7.5 Cubic Ring System
171(2)
7.6 Hyperlabyrinth System
173(1)
7.7 Circulant Neural Networks
174(2)
7.8 Hyperviscous Ring
176(1)
7.9 Rings of Oscillators
176(9)
7.9.1 Coupled pendulums
177(1)
7.9.2 Coupled cubic oscillators
177(1)
7.9.3 Coupled signum oscillators
178(1)
7.9.4 Coupled van der Pol oscillators
179(1)
7.9.5 Coupled FitzHugh-Nagumo oscillators
180(2)
7.9.6 Coupled complex oscillators
182(1)
7.9.7 Coupled Lorenz systems
182(3)
7.9.8 Coupled jerk systems
185(1)
7.10 Star Systems
185(10)
7.10.1 Coupled pendulums
187(1)
7.10.2 Coupled cubic oscillators
187(1)
7.10.3 Coupled signum oscillators
188(2)
7.10.4 Coupled van der Pol oscillators
190(1)
7.10.5 Coupled FitzHugh-Nagumo oscillators
191(1)
7.10.6 Coupled complex oscillators
191(2)
7.10.7 Coupled diffusionless Lorenz systems
193(1)
7.10.8 Coupled jerk systems
194(1)
8 Spatiotemporal Systems
195(26)
8.1 Numerical Methods
195(4)
8.2 Kuramoto-Sivashinsky Equation
199(1)
8.3 Kuramoto-Sivashinsky Variants
200(1)
8.3.1 Cubic case
201(1)
8.3.2 Quartic case
201(1)
8.4 Chaotic Traveling Waves
201(3)
8.4.1 Rotating Kuramoto-Sivashinsky system
203(1)
8.4.2 Rotating Kuramoto-Sivashinsky variant
203(1)
8.5 Continuum Ring Systems
204(8)
8.5.1 Quadratic ring system
204(1)
8.5.2 Antisymmetric quadratic system
205(2)
8.5.3 Other simple PDEs
207(5)
8.6 Traveling Wave Variants
212(9)
9 Time-Delay Systems
221(12)
9.1 Delay Differential Equations
221(2)
9.2 Mackey-Glass Equation
223(1)
9.3 IkedaDDE
223(2)
9.4 Sinusoidal DDE
225(1)
9.5 Polynomial DDE
225(2)
9.6 Sigmoidal DDE
227(1)
9.7 SignumDDE
227(2)
9.8 Piecewise-linear DDEs
229(3)
9.8.1 Antisymmetric case
229(1)
9.8.2 Asymmetric case
229(1)
9.8.3 Asymmetric logistic DDE
230(2)
9.9 Asymmetric Logistic DDE with Continuous Delay
232(1)
10 Chaotic Electrical Circuits
233(32)
10.1 Circuit Elegance
233(1)
10.2 Forced Relaxation Oscillator
234(3)
10.3 Autonomous Relaxation Oscillator
237(2)
10.4 Coupled Relaxation Oscillators
239(3)
10.4.1 Two oscillators
239(2)
10.4.2 Many oscillators
241(1)
10.5 Forced Diode Resonator
242(1)
10.6 Saturating Inductor Circuit
243(3)
10.7 Forced Piecewise-linear Circuit
246(1)
10.8 Chua's Circuit
246(3)
10.9 Nishio's Circuit
249(2)
10.10 Wien-bridge Oscillator
251(3)
10.11 Jerk Circuits
254(5)
10.11.1 Absolute-value case
254(1)
10.11.2 Single-knee case
255(1)
10.11.3 Signum case
256(2)
10.11.4 Signum variant
258(1)
10.12 Master-slave Oscillator
259(2)
10.13 Ring of Oscillators
261(2)
10.14 Delay-line Oscillator
263(2)
Bibliography 265(16)
Index 281
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