Elegant Chaos : Algebraically Simple Chaotic Flows.

By: Sprott, Julien ClintonMaterial type: TextTextPublisher: Singapore : World Scientific Publishing Co Pte Ltd, 2010Copyright date: ©2010Description: 1 online resource (304 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9789812838827Subject(s): Chaotic behavior in systems -- Mathematics | Flows (Differentiable dynamical systems) | Lyapunov exponentsGenre/Form: Electronic books.Additional physical formats: Print version:: Elegant Chaos : Algebraically Simple Chaotic FlowsDDC classification: 515.35 LOC classification: QA614.82.S67 2010Online resources: Click to View
Contents:
Intro -- Contents -- Preface -- List of Tables -- 1. Fundamentals -- 1.1 Dynamical Systems -- 1.2 State Space -- 1.3 Dissipation -- 1.4 Limit Cycles -- 1.5 Chaos and Strange Attractors -- 1.6 Poincare Sections and Fractals -- 1.7 Conservative Chaos -- 1.8 Two-toruses and Quasiperiodicity -- 1.9 Largest Lyapunov Exponent -- 1.10 Lyapunov Exponent Spectrum -- 1.11 Attractor Dimension -- 1.12 Chaotic Transients -- 1.13 Intermittency -- 1.14 Basins of Attraction -- 1.15 Numerical Methods -- 1.16 Elegance -- 2. Periodically Forced Systems -- 2.1 Van der Pol Oscillator -- 2.2 Rayleigh Oscillator -- 2.3 Rayleigh Oscillator Variant -- 2.4 Du±ng Oscillator -- 2.5 Quadratic Oscillators -- 2.6 Piecewise-linear Oscillators -- 2.7 Signum Oscillators -- 2.8 Exponential Oscillators -- 2.9 Other Undamped Oscillators -- 2.10 Velocity Forced Oscillators -- 2.11 Parametric Oscillators -- 2.12 Complex Oscillators -- 3. Autonomous Dissipative Systems -- 3.1 Lorenz System -- 3.2 Diffusionless Lorenz System -- 3.3 RÄossler System -- 3.4 Other Quadratic Systems -- 3.4.1 RÄossler prototype-4 system -- 3.4.2 Sprott systems -- 3.5 Jerk Systems -- 3.5.1 Simplest quadratic case -- 3.5.2 Rational jerks -- 3.5.3 Cubic cases -- 3.5.4 Cases with arbitrary power -- 3.5.5 Piecewise-linear case -- 3.5.6 Memory oscillators -- 3.6 Circulant Systems -- 3.6.1 Halvorsen's system -- 3.6.2 Thomas' systems -- 3.6.3 Piecewise-linear system -- 3.7 Other Systems -- 3.7.1 Multiscroll systems -- 3.7.2 Lotka-Volterra systems -- 3.7.3 Chua's systems -- 3.7.4 Rikitake dynamo -- 4. Autonomous Conservative Systems -- 4.1 Nos-Hoover Oscillator -- 4.2 Nos-Hoover Variants -- 4.3 Jerk Systems -- 4.3.1 Jerk form of the Nos-Hoover oscillator -- 4.3.2 Simplest conservative chaotic flow -- 4.3.3 Other conservative jerk systems -- 4.4 Circulant Systems -- 4.4.1 Quadratic case -- 4.4.2 Cubic case.
4.4.3 Labyrinth chaos -- 4.4.4 Piecewise-linear system -- 5. Low-dimensional Systems (D 3) -- 6.1 Periodically Forced Systems -- 6.1.1 Forced pendulum -- 6.1.2 Other forced nonlinear oscillators -- 6.2 Master-slave Oscillators -- 6.3 Mutually Coupled Nonlinear Oscillator -- 6.3.1 Coupled pendulums -- 6.3.2 Coupled van der Pol oscillators -- 6.3.3 Coupled FitzHugh-Nagumo oscillators -- 6.3.4 Coupled complex oscillators -- 6.3.5 Other coupled nonlinear oscillators -- 6.4 Hamiltonian Systems -- 6.4.1 Coupled nonlinear oscillators -- 6.4.2 Velocity coupled oscillators -- 6.4.3 Parametrically coupled oscillators -- 6.4.4 Simplest Hamiltonian -- 6.4.5 Henon-Heiles system -- 6.4.6 Reduced Henon-Heiles system -- 6.4.7 N-body gravitational systems -- 6.4.7.1 Three-body problem -- 6.4.7.2 Restricted three-body problem -- 6.4.8 N-body Coulomb systems -- 6.4.8.1 Three spatial dimensions -- 6.4.8.2 Two spatial dimensions -- 6.5 Anti-Newtonian Systems -- 6.5.1 Two-body problem -- 6.5.2 Three-body problem -- 6.6 Hyperjerk Systems -- 6.6.1 Forced oscillators -- 6.6.2 Chlouverakis systems -- 6.6.2.1 Snap systems -- 6.6.2.2 Crackle systems -- 6.6.2.3 Pop systems -- 6.7 Hyperchaotic Systems -- 6.7.1 Rossler hyperchaos -- 6.7.2 Snap hyperchaos -- 6.7.3 Coupled chaotic systems -- 6.7.4 Other hyperchaotic systems -- 6.8 Autonomous Complex Systems -- 6.9 Lotka-Volterra Systems -- 6.10 Artificial Neural Networks -- 6.10.1 Minimal dissipative artificial neural network -- 6.10.2 Minimal conservative artificial neural network -- 6.10.3 Minimal circulant artificial neural network -- 7. Circulant Systems -- 7.1 Lorenz-Emanuel System -- 7.2 Lotka-Volterra Systems -- 7.3 Antisymmetric Quadratic System -- 7.4 Quadratic Ring System -- 7.5 Cubic Ring System.
7.6 Hyperlabyrinth System -- 7.7 Circulant Neural Networks -- 7.8 Hyperviscous Ring -- 7.9 Rings of Oscillators -- 7.9.1 Coupled pendulums -- 7.9.2 Coupled cubic oscillators -- 7.9.3 Coupled signum oscillators -- 7.9.4 Coupled van der Pol oscillators -- 7.9.5 Coupled FitzHugh-Nagumo oscillators -- 7.9.6 Coupled complex oscillators -- 7.9.7 Coupled Lorenz systems -- 7.9.7.1 Viscously coupled case -- 7.9.7.2 Diffusively coupled case -- 7.9.7.3 Coupled diffusionless case -- 7.9.8 Coupled jerk systems -- 7.10 Star Systems -- 7.10.1 Coupled pendulums -- 7.10.2 Coupled cubic oscillators -- 7.10.3 Coupled signum oscillators -- 7.10.4 Coupled van der Pol oscillators -- 7.10.5 Coupled FitzHugh-Nagumo oscillators -- 7.10.6 Coupled complex oscillators -- 7.10.7 Coupled diffusionless Lorenz systems -- 7.10.8 Coupled jerk systems -- 8. Spatiotemporal Systems -- 8.1 Numerical Methods -- 8.2 Kuramoto-Sivashinsky Equation -- 8.3 Kuramoto-Sivashinsky Variants -- 8.3.1 Cubic case -- 8.3.2 Quartic case -- 8.4 Chaotic Traveling Waves -- 8.4.1 Rotating Kuramoto-Sivashinsky system -- 8.4.2 Rotating Kuramoto-Sivashinsky variant -- 8.5 Continuum Ring Systems -- 8.5.1 Quadratic ring system -- 8.5.2 Antisymmetric quadratic system -- 8.5.3 Other simple PDEs -- 8.6 Traveling Wave Variants -- 9. Time-Delay Systems -- 9.1 Delay Differential Equations -- 9.2 Mackey-Glass Equation -- 9.3 Ikeda DDE -- 9.4 Sinusoidal DDE -- 9.5 Polynomial DDE -- 9.6 Sigmoidal DDE -- 9.7 Signum DDE -- 9.8 Piecewise-linear DDEs -- 9.8.1 Antisymmetric case -- 9.8.2 Asymmetric case -- 9.8.3 Asymmetric logistic DDE -- 9.9 Asymmetric Logistic DDE with Continuous Delay -- 10. Chaotic Electrical Circuits -- 10.1 Circuit Elegance -- 10.2 Forced Relaxation Oscillator -- 10.3 Autonomous Relaxation Oscillator -- 10.4 Coupled Relaxation Oscillators -- 10.4.1 Two oscillators -- 10.4.2 Many oscillators.
10.5 Forced Diode Resonator -- 10.6 Saturating Inductor Circuit -- 10.7 Forced Piecewise-linear Circuit -- 10.8 Chua's Circuit -- 10.9 Nishio's Circuit -- 10.10 Wien-bridge Oscillator -- 10.11 Jerk Circuits -- 10.11.1 Absolute-value case -- 10.11.2 Single-knee case -- 10.11.3 Signum case -- 10.11.4 Signum variant -- 10.12 Master-slave Oscillator -- 10.13 Ring of Oscillators -- 10.14 Delay-line Oscillator -- Bibliography -- Index.
Summary: Key Features:Includes an introductory chapter on fundamentals, which makes the book self-contained and suitable for readers with little previous knowledge of the subjectAssumes only an elementary knowledge of calculus.
Tags from this library: No tags from this library for this title. Log in to add tags.
    Average rating: 0.0 (0 votes)
No physical items for this record

Intro -- Contents -- Preface -- List of Tables -- 1. Fundamentals -- 1.1 Dynamical Systems -- 1.2 State Space -- 1.3 Dissipation -- 1.4 Limit Cycles -- 1.5 Chaos and Strange Attractors -- 1.6 Poincare Sections and Fractals -- 1.7 Conservative Chaos -- 1.8 Two-toruses and Quasiperiodicity -- 1.9 Largest Lyapunov Exponent -- 1.10 Lyapunov Exponent Spectrum -- 1.11 Attractor Dimension -- 1.12 Chaotic Transients -- 1.13 Intermittency -- 1.14 Basins of Attraction -- 1.15 Numerical Methods -- 1.16 Elegance -- 2. Periodically Forced Systems -- 2.1 Van der Pol Oscillator -- 2.2 Rayleigh Oscillator -- 2.3 Rayleigh Oscillator Variant -- 2.4 Du±ng Oscillator -- 2.5 Quadratic Oscillators -- 2.6 Piecewise-linear Oscillators -- 2.7 Signum Oscillators -- 2.8 Exponential Oscillators -- 2.9 Other Undamped Oscillators -- 2.10 Velocity Forced Oscillators -- 2.11 Parametric Oscillators -- 2.12 Complex Oscillators -- 3. Autonomous Dissipative Systems -- 3.1 Lorenz System -- 3.2 Diffusionless Lorenz System -- 3.3 RÄossler System -- 3.4 Other Quadratic Systems -- 3.4.1 RÄossler prototype-4 system -- 3.4.2 Sprott systems -- 3.5 Jerk Systems -- 3.5.1 Simplest quadratic case -- 3.5.2 Rational jerks -- 3.5.3 Cubic cases -- 3.5.4 Cases with arbitrary power -- 3.5.5 Piecewise-linear case -- 3.5.6 Memory oscillators -- 3.6 Circulant Systems -- 3.6.1 Halvorsen's system -- 3.6.2 Thomas' systems -- 3.6.3 Piecewise-linear system -- 3.7 Other Systems -- 3.7.1 Multiscroll systems -- 3.7.2 Lotka-Volterra systems -- 3.7.3 Chua's systems -- 3.7.4 Rikitake dynamo -- 4. Autonomous Conservative Systems -- 4.1 Nos-Hoover Oscillator -- 4.2 Nos-Hoover Variants -- 4.3 Jerk Systems -- 4.3.1 Jerk form of the Nos-Hoover oscillator -- 4.3.2 Simplest conservative chaotic flow -- 4.3.3 Other conservative jerk systems -- 4.4 Circulant Systems -- 4.4.1 Quadratic case -- 4.4.2 Cubic case.

4.4.3 Labyrinth chaos -- 4.4.4 Piecewise-linear system -- 5. Low-dimensional Systems (D 3) -- 6.1 Periodically Forced Systems -- 6.1.1 Forced pendulum -- 6.1.2 Other forced nonlinear oscillators -- 6.2 Master-slave Oscillators -- 6.3 Mutually Coupled Nonlinear Oscillator -- 6.3.1 Coupled pendulums -- 6.3.2 Coupled van der Pol oscillators -- 6.3.3 Coupled FitzHugh-Nagumo oscillators -- 6.3.4 Coupled complex oscillators -- 6.3.5 Other coupled nonlinear oscillators -- 6.4 Hamiltonian Systems -- 6.4.1 Coupled nonlinear oscillators -- 6.4.2 Velocity coupled oscillators -- 6.4.3 Parametrically coupled oscillators -- 6.4.4 Simplest Hamiltonian -- 6.4.5 Henon-Heiles system -- 6.4.6 Reduced Henon-Heiles system -- 6.4.7 N-body gravitational systems -- 6.4.7.1 Three-body problem -- 6.4.7.2 Restricted three-body problem -- 6.4.8 N-body Coulomb systems -- 6.4.8.1 Three spatial dimensions -- 6.4.8.2 Two spatial dimensions -- 6.5 Anti-Newtonian Systems -- 6.5.1 Two-body problem -- 6.5.2 Three-body problem -- 6.6 Hyperjerk Systems -- 6.6.1 Forced oscillators -- 6.6.2 Chlouverakis systems -- 6.6.2.1 Snap systems -- 6.6.2.2 Crackle systems -- 6.6.2.3 Pop systems -- 6.7 Hyperchaotic Systems -- 6.7.1 Rossler hyperchaos -- 6.7.2 Snap hyperchaos -- 6.7.3 Coupled chaotic systems -- 6.7.4 Other hyperchaotic systems -- 6.8 Autonomous Complex Systems -- 6.9 Lotka-Volterra Systems -- 6.10 Artificial Neural Networks -- 6.10.1 Minimal dissipative artificial neural network -- 6.10.2 Minimal conservative artificial neural network -- 6.10.3 Minimal circulant artificial neural network -- 7. Circulant Systems -- 7.1 Lorenz-Emanuel System -- 7.2 Lotka-Volterra Systems -- 7.3 Antisymmetric Quadratic System -- 7.4 Quadratic Ring System -- 7.5 Cubic Ring System.

7.6 Hyperlabyrinth System -- 7.7 Circulant Neural Networks -- 7.8 Hyperviscous Ring -- 7.9 Rings of Oscillators -- 7.9.1 Coupled pendulums -- 7.9.2 Coupled cubic oscillators -- 7.9.3 Coupled signum oscillators -- 7.9.4 Coupled van der Pol oscillators -- 7.9.5 Coupled FitzHugh-Nagumo oscillators -- 7.9.6 Coupled complex oscillators -- 7.9.7 Coupled Lorenz systems -- 7.9.7.1 Viscously coupled case -- 7.9.7.2 Diffusively coupled case -- 7.9.7.3 Coupled diffusionless case -- 7.9.8 Coupled jerk systems -- 7.10 Star Systems -- 7.10.1 Coupled pendulums -- 7.10.2 Coupled cubic oscillators -- 7.10.3 Coupled signum oscillators -- 7.10.4 Coupled van der Pol oscillators -- 7.10.5 Coupled FitzHugh-Nagumo oscillators -- 7.10.6 Coupled complex oscillators -- 7.10.7 Coupled diffusionless Lorenz systems -- 7.10.8 Coupled jerk systems -- 8. Spatiotemporal Systems -- 8.1 Numerical Methods -- 8.2 Kuramoto-Sivashinsky Equation -- 8.3 Kuramoto-Sivashinsky Variants -- 8.3.1 Cubic case -- 8.3.2 Quartic case -- 8.4 Chaotic Traveling Waves -- 8.4.1 Rotating Kuramoto-Sivashinsky system -- 8.4.2 Rotating Kuramoto-Sivashinsky variant -- 8.5 Continuum Ring Systems -- 8.5.1 Quadratic ring system -- 8.5.2 Antisymmetric quadratic system -- 8.5.3 Other simple PDEs -- 8.6 Traveling Wave Variants -- 9. Time-Delay Systems -- 9.1 Delay Differential Equations -- 9.2 Mackey-Glass Equation -- 9.3 Ikeda DDE -- 9.4 Sinusoidal DDE -- 9.5 Polynomial DDE -- 9.6 Sigmoidal DDE -- 9.7 Signum DDE -- 9.8 Piecewise-linear DDEs -- 9.8.1 Antisymmetric case -- 9.8.2 Asymmetric case -- 9.8.3 Asymmetric logistic DDE -- 9.9 Asymmetric Logistic DDE with Continuous Delay -- 10. Chaotic Electrical Circuits -- 10.1 Circuit Elegance -- 10.2 Forced Relaxation Oscillator -- 10.3 Autonomous Relaxation Oscillator -- 10.4 Coupled Relaxation Oscillators -- 10.4.1 Two oscillators -- 10.4.2 Many oscillators.

10.5 Forced Diode Resonator -- 10.6 Saturating Inductor Circuit -- 10.7 Forced Piecewise-linear Circuit -- 10.8 Chua's Circuit -- 10.9 Nishio's Circuit -- 10.10 Wien-bridge Oscillator -- 10.11 Jerk Circuits -- 10.11.1 Absolute-value case -- 10.11.2 Single-knee case -- 10.11.3 Signum case -- 10.11.4 Signum variant -- 10.12 Master-slave Oscillator -- 10.13 Ring of Oscillators -- 10.14 Delay-line Oscillator -- Bibliography -- Index.

Key Features:Includes an introductory chapter on fundamentals, which makes the book self-contained and suitable for readers with little previous knowledge of the subjectAssumes only an elementary knowledge of calculus.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

There are no comments on this title.

to post a comment.

Powered by Koha