In this chapter we shall describe some of the basic techniques used in the numerical
analysis of dynamical systems. We assume that low-level numerical routines like those for …

The theory of dynamical systems studies the behavior of solutions of systems, like nonlinear
ordinary differential equations (ODEs), depending upon parameters. Using qualitative …

Fifteen years have elapsed after the second edition of Practical Bifurcation and Stability
Analysis was published. During that time period the? eld of computational bifurcation has …

The theoretical point of view may be viewed as\classical", but it is constructive and
applicable to numerical computation. Most current presentations of bifurcation theory rely on …

" Dissipative structures" is a concept which has recently been used in physics to discuss the
formation of structures organized in space and/or time at the expense of the energy flowing …

In this paper, we explain how to compute bifurcation parameter values of periodic solutions
for non-autonomous nonlinear differential equations. Although various approaches and …

The purpose of this paper is to give an account of recent developments in numerical
methods for the solution of bifurcation problems. For readers not too familiar with our subject …

Analytical methods of bifurcation theory and numerical path-following methods complement
each other in many investigations of nonlinear systems. This brief “state of the art” review …

This book describes numerical methods for the detection, computation, and continuation
(following paths) of equilibria and bifurcation points of equilibria of dynamical systems. In the …

The objectives and some basic methods of numerical bifurcation analysis are described.
Several computational examples are used to illustrate the power as well as the limitations of …