Numerical Bifurcation Analysis for Dynamical Systems

Abstract

This survey reviews the numerical bifurcation analysis for dynamical systems and explains the pseudo-arclength continuation and detection and location methods for a bifurcation point. Moreover, locating methods for periodic and homoclinic solutions of ordinary differential equations are described. As a more advanced topic, the parameterization method for locating a quasiperiodic closed invariant curve for discrete-time dynamical systems is discussed. Finally, an application of these methods to the numerical continuation of rippling rectangular waves for the modified Benney equation is introduced.