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Bifurcations of periodic solutions of ODEs using bordered systems. (English) Zbl 1060.65677
Psihoyios, G. (ed.), NACoM-2003 extended abstracts. Proceedings of the international conference on numerical analysis and computational mathematics, Cambridge, UK, May 23–26, 2003. (Contained as No. 2 in the journal ANACM 1, No. 1-2, 524 p. (2004)). Weinheim: Wiley-VCH (ISBN 3-527-40462-7). 61-64 (2004).
Summary: We discuss the numerical computation and continuation of the fold, flip and Naimark-Sacker bifurcations of periodic solutions of ODEs. We use minimal extended systems based on bordered operators between function spaces. These are discretized by a method based on orthogonal collocation. The bordering functions and vectors of the continuous problem correspond to bordering vectors of the discretized matrices. We discuss the implementation of these methods in the Matlab software packages matcont and cl$$_-$$matcont.
For the entire collection see [Zbl 1053.65003].

##### MSC:
 65P30 Numerical bifurcation problems 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems 37M20 Computational methods for bifurcation problems in dynamical systems
##### Keywords:
bifurcations; periodic solutions; collocation
MATCONT; Matlab