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

Maoan Han; Valery G. Romanovski

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

Classical Analysis and ODEs 2011-09-30 v1

Authors: Maoan Han , Valery G. Romanovski

Abstract

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.

Keywords

limit cycle bifurcations nilpotent focus nilpotent center Poincare return map generalized focal values planar systems lower and upper bounds

Cite

@article{arxiv.1109.6473,
  title  = {Limit cycle bifurcations from a nilpotent focus or center of planar systems},
  author = {Maoan Han and Valery G. Romanovski},
  journal= {arXiv preprint arXiv:1109.6473},
  year   = {2011}
}

Comments

This paper was submitted to Journal of Mathematical Analysis and Applications

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