Numerical continuation of fold bifurcations of limit cycles in MATCONT

Abstract

MATCONT is a Matlab continuation package with a GUI for the interactive numerical study of a range of parameterized nonlinear problems. In the case of ODEs it allows to compute curves of equilibria, limit points, Hopf points, limit cycles, period doubling bifurcation points of limit cycles and fold bifurcation points of limit cycles. It can use the symbolic toolbox of Matlab to compute derivatives of order up to five of the object function. We discuss some details on the implementation of the limit cycles and the fold bifurcation of limit cycles in MATCONT. The inherent sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by using the standard Matlab sparse matrix methods. © Springer-Verlag Berlin Heidelberg 2003.