Continuation and Bifurcation software in MATLAB

Abstract

This article contains discussions of the algorithms used for the construction of the continuation software implemented in this thesis. The aim of the continuation was to be able to perform continuation of equilibria and periodic solutions originating from a Hopf bifurcation point. Algorithms for detection of simple branch points, folds, and Hopf bifurcation points have also been implemented. Some considerations are made with regard to optimization, and two schemes for mesh adaptation of periodic solutions based on moving mesh equations are suggested.