Limit Cycle Bifurcations from a Nilpotent Focus or Center of Planar Systems

作者：Han, Maoan^*; Romanovski, Valery G.

来源：Abstract and Applied Analysis, 2012, 720830.

DOI：10.1155/2012/720830

We study analytic properties of the Poincare return map and generalized focal values of analytic planar systems with a nilpotent focus or center. We use the focal values and the map to study the number of limit cycles of this kind of systems and obtain some new results on the lower and upper bounds of the maximal number of limit cycles bifurcating from the nilpotent focus or center. The main results generalize the classical Hopf bifurcation theory and establish the new bifurcation theory for the nilpotent case.

• 出版日期2012
• 单位上海师范大学