Introduction to Dynamical Systems.- Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems.- One-Parameter Bifurcations of Equilibria in Continuous-Time Systems.- One-Parameter Bifurcations of Fixed Points in Discrete-Time Systems.- Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Systems.- Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria.- Other One-Parameter Bifurcations in Continuous-Time Systems.- Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems.- Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems.- Numerical Analysis of Bifurcations.- A: Basic Notions from Algebra, Analysis, and Geometry.- References.- Index.
Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.
From Reviews of the First Edition: "I know of no other book that so clearly explains the basic phenomena of bifurcation theory." -Mathematical Reviews
This book provides a student or researcher with a solid basis in nonlinear dynamical systems and their bifurcations, giving them the necessary understanding of the approaches, methods, results and terminology used in the modern applied mathematics literature. It covers the basic topics of the bifurcation theory and can help in composing a course on nonlinear dynamical systems or system theory. This new edition preserves the structure of the previous edition, while updating the context to incorporate recent theoretical and software developments, in particular new and improved numerical methods for bifurcation analysis.