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.