On the bifurcation of periodic orbits

Details On the bifurcation of periodic orbits On the bifurcation of periodic orbits

2001-10-11

arxiv.org/abs/math/0110121v1

Mathematics

Dynamical Systems

Scientific paper

This article is a survey on recent contributions to an effective version of Bautin's theory about the bifurcation of periodic orbits (limit cycles). The analysis of Hopf bifurcations of higher order is possible by use of the return mapping. Explicit estimates of the size of the domain on which the number of limit cycles is controlled are important in many applications of bifurcation theory (for instance in Biology and Physiology).

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