Chaotic Modelling and Simulation: Analysis of Chaotic Models, Attractors and Forms

Introduction Chaos in Differential Equations Systems Chaos in Difference Equation Systems More Complex Structures Chaos and the Universe Odds and Ends and Milestones Models and Modeling Introduction Model Construction Modeling Techniques Chaotic Analysis and Simulation Deterministic, Stochastic, and Chaotic Models The Logistic Model The Logistic Map The Bifurcation Diagram Other Models with Similar Behavior Models with Different Chaotic Behavior The GRM1 Chaotic Model Further Discussion The Delay Logistic Model Introduction Delay Difference Models Time Delay Differential Equations A More Complicated Delay Model A Delay Differential Logistic Analogue Other Delay Logistic Models Model Behavior for Large Delays Another Delay Logistic Model The Henon Model Global Period Doubling Bifurcations in the Henon Map The Cosine-Henon Model An Example of Bifurcation and Period Doubling A Differential Equation Analogue Variants of the Henon Delay Difference Equation Variants of the Henon System Equations The Holmes and Sine Delay Models Three-Dimensional and Higher-Dimensional Models Equilibrium Points and Characteristic Matrices The Lotka-Volterra Model The Arneodo Model An Autocatalytic Attractor A Four-Dimensional Autocatalytic Attractor The Rossler Model The Lorenz Model Nonchaotic Systems Conservative Systems Linear Systems Egg-Shaped Forms Symmetric Forms More Complex Forms Higher-Order Forms Rotations Introduction A Simple Rotation-Translation System of Differential Equations A Discrete Rotation-Translation Model A General Rotation-Translation Model Rotating Particles inside the Egg-Shaped Form Rotations Following an Inverse Square Law Shape and Form Introduction Isometries in Modeling Reflection and Translation Application in the Ikeda Attractor Chaotic Attractors and Rotation-Reflection Experimenting with Rotation and Reflection Chaotic Circular Forms Further Analysis Chaotic Advection The Sink Problem Noncentral Sink Two Symmetric Sinks Chaotic Forms without Space Contraction Other Chaotic Forms Complex Sinusoidal Rotation Angle A Special Rotation-Translation Model Other Rotation-Translation Models Chaos in Galaxies and Related Simulations Introduction Chaos in the Solar System Galaxy Models and Modeling Rotation-Reflection Relativity in Rotation-Translation Systems Other Relativistic Forms Galactic Clusters Relativistic Reflection-Translation Rotating Disks of Particles Rotating Particles under Distant Attracting Masses Two Equal Attracting Masses in Opposite Directions Galactic-Type Potentials and the Henon-Heiles System Introduction The Henon-Heiles System Discrete Analogues to the Henon-Heiles System Paths of Particles in the Henon-Heiles System Other Forms for the Hamiltonian The Simplest Form for the Hamiltonian Gravitational Attraction A Logarithmic Potential Hamiltonians with a Galactic Type Potential: The Contopoulos System Another Simple Hamiltonian System Odds and Ends Forced Nonlinear Oscillators The Effect of Noise in Three-Dimensional Models The Lotka-Volterra Theory for the Growth of Two Conflicting Populations The Pendulum A Special Second-Order Differential Equation Other Patterns and Chaotic Forms Milestones References List of Figures Index