Elements of Applied Bifurcation Theory

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.

Table of Contents

1 Introduction to Dynamical Systems

2 Topological Equivalence, Bifurcations, and St ructural Stability of Dynamical Systems

3 One-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems

4 One-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems

5 Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Dynamical Systems

6 Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria

7 Other One-Parameter Bifurcations in Continuous-Time Dynamical Systems

8 Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems

9 Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems

10 Numerical Analysis of Bifurcations

Appendix A: Basic Notions from Algebra, Analysis, and Geometry

Table of Contents

Yuri A. Kuznetsov is a Russian-American mathematician currently the M. D. Anderson Chair Professor of Mathematics at University of Houston and Editor-in-Chief of Journal of Numerical Mathematics.A