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Numerical Continuation of Fold Bifurcations of Limit Cycles in MATCONT
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Numerical Continuation of Fold Bifurcations of Limit Cycles in MATCONT
Annick Dhooge6 , Willy Govaerts6 and Yuri A. Kuznetsov7 
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Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium |
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Mathematisch Instituut, Universiteit Utrecht, Boedapestlaan 6, 3584 CD Utrecht, The Netherlands |
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.
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