Limit cycle bifurcations in a class of perturbed piecewise smooth systems

作者：Xiong, Yanqin; Han, Maoan^*

来源：Applied Mathematics and Computation, 2014, 242: 47-64.

DOI：10.1016/j.amc.2014.05.035

• Piecewise perturbed Hamiltonian system
• Hopf bifurcation
• Generalized homoclinic loop
• Phase portrait

In this paper, we concern with the number of limit cycles in a piecewise polynomial system. First, we give 42 different phase portraits of the unperturbed system with at least one closed orbit. Then, we perturb one phase portrait of them by piecewise polynomials, and consider lower bounds for the maximal numbers of limit cycles emerging from the origin and generalized homoclinic loop, respectively.

• 出版日期2014-9-1
• 单位上海师范大学