Limit cycle bifurcations from a nilpotent focus or center of planar systems

Details Limit cycle bifurcations from a nilpotent focus or center of planar systems Limit cycle bifurcations from a nilpotent focus or center of planar systems

2011-09-29

arxiv.org/abs/1109.6473v1

Mathematics

Classical Analysis and ODEs

This paper was submitted to Journal of Mathematical Analysis and Applications

Scientific paper

In this paper, we study the analytical property of the Poincare return map and the generalized focal values of an analytical planar system with a nilpotent focus or center. Then we use the focal values and the map to study the number of limit cycles of this kind of systems with parameters, and obtain some new results on the lower and upper bounds of the maximal number of limit cycles near the nilpotent focus or center.

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