Global bifurcations in dynamical systems often occur from homoclinic or heteroclinic orbits.
The best known effect is the termination of a branch of periodic orbits at a homoclinic orbit. In …

We discuss new and improved algorithms for the bifurcation analysis of fixed points and
periodic orbits (cycles) of maps and their implementation in matcont, a MATLAB toolbox for …

We present a numerical technique for the analysis of local bifurcations which is based on the
continuation of structurally unstable invariant sets in a suitable phase-parameter space. The …

It is well known that bifurcation points are usually quite sensitive to perturbations. For
example, introducing an imperfection in a bifurcation problem may turn two intersecting …

A number of basic algorithms for the numerical analysis and control of bifurcation
phenomena are described. The emphasis is on algorithms based on pseudoarclength …

This book was intended as an introduction to the topic of numerical continuation which
would be accessible to a readership of widely varying mathematical backgrounds. Realizing …

The qualitative behaviour of iterates of a map can be very complicated. One approach to
these phenomena starts with the simplest situation, the case where the map has a fixed …

Various types of bifurcation phenomena may be observed in problems of stability limit or
loss of stability of nonlinear physical systems. We will consider in this paper a special type of …

We present the set of bifurcation tracking algorithms which have been developed in the
LOCA software library to work with large scale application codes that use fully coupled …

Symmetry is a property which occurs throughout nature and it is therefore natural that
symmetry should be considered when attempting to model nature. In many cases, these …