Order Now from World Scientific Buy from World Scientific Buy from Amazon.com Buy from Barnes & Noble World Scientific, 2010 · 356 pages World Scientific Series on Nonlinear Science, Series A ISBN 978-981-4307-74-1 (hardcover) ISBN 978-981-4464-79-6 (ebook) Rigorous proofs of chaos and bifurcations — not just numerical evidence The Hénon map and the full family of 2-D quadratic maps, classified into 30 maps Regions of chaos, hyperchaos and non-chaos in parameter space Chua's double-scroll circuit proved chaotic two ways, including a computer-assisted proof

2-D Quadratic Maps and 3-D ODE Systems A Rigorous Approach Elhadj Zeraoulia and J. C. Sprott Emeritus Professor of Physics, University of Wisconsin–Madison Praise for 2-D Quadratic Maps and 3-D ODE Systems "As a reader in favor of tradition in mathematics, I find attractive the approach based on examples." — Mathematical Reviews "The book is generously illustrated; each chapter contains a short section with exercises for independent study. The monograph concludes with an exhaustive list of references and a concise index. It is a useful source for information specialists and graduate students working with the theory and applications of dynamical systems." — Zentralblatt MATH About the Book This book is based on research on the rigorous proof of chaos and bifurcations in 2-D quadratic maps, especially the invertible case such as the Hénon map, and in 3-D ODEs, especially piecewise linear systems such as Chua's circuit. It also covers recent work on general 2-D quadratic maps, especially their classification into equivalence classes, and finding regions for chaos, hyperchaos, and non-chaos in the space of bifurcation parameters. After an introduction to the rigorous tools used to prove chaos and bifurcations, the book studies the invertible 2-D quadratic map and classifies 2-D quadratic maps into 30 maps with well-known formulas. Two proofs on the regions for chaos, hyperchaos, and non-chaos are presented using a technique based on the second-derivative test and bounds for Lyapunov exponents. Chaos in the piecewise linear Chua system is proved by two methods, one based on a Poincaré map and one computer-assisted, followed by a rigorous analysis of its bifurcation phenomena. Contents 1. Tools for the Rigorous Proof of Chaos and Bifurcations 2. 2-D Quadratic Maps: The Invertible Case 3. Classification of Chaotic Orbits of the General 2-D Quadratic Map 4. Rigorous Proof of Chaos in the Double Scroll System 5. Rigorous Analysis of Bifurcation Phenomena

Last updated October 25, 2026