Offers Both Standard and Novel Approaches for the Modeling of Systems
Examines the Interesting Behavior of Particular Classes of Models
Chaotic Modelling and Simulation: Analysis of Chaotic Models, Attractors and Forms presents the main models developed by pioneers of chaos theory, along with new extensions and variations of these models. Using more than 500 graphs and illustrations, the authors show how to design, estimate, and test an array of models.
Requiring little prior knowledge of mathematics, the book focuses on classical forms and attractors as well as new simulation methods and techniques. Ideas clearly progress from the most elementary to the most advanced. The authors cover deterministic, stochastic, logistic, Gaussian, delay, Hénon, Holmes, Lorenz, Rössler, and rotation models. They also look at chaotic analysis as a tool to design forms that appear in physical systems; simulate complicated and chaotic orbits and paths in the solar system; explore the Hénon–Heiles, Contopoulos, and Hamiltonian systems; and provide a compilation of interesting systems and variations of systems, including the very intriguing Lotka–Volterra system.
Making a complex topic accessible through a visual and geometric style, this book should inspire new developments in the field of chaotic models and encourage more readers to become involved in this rapidly advancing area.
Introduction. Models and Modeling. The Logistic Model. The Delay Logistic Model. The Hénon Model. Three-Dimensional and Higher-Dimensional Models. Nonchaotic Systems. Rotations. Shape and Form. Chaotic Advection. Chaos in Galaxies and Related Simulations. Galactic-Type Potentials and the Hénon–Heiles System. Odds and Ends. Milestones. References. List of Figures. Index.