ELEMENTS OF APPLIED BIFURCATION THEORY

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.