Limit Cycle Bifurcations by Perturbing a Piecewise Hamiltonian System with a Double Homoclinic Loop

作者：Xiong, Yanqin^*

来源：International Journal of Bifurcation and Chaos, 2016, 26(6): 1650103.

DOI：10.1142/S0218127416501030

• Piecewise
• double homoclinic loop
• Hamiltonian system
• Lienard system

This paper is concerned with the bifurcation problem of limit cycles by perturbing a piecewise Hamiltonian system with a double homoclinic loop. First, the derivative of the first Melnikov function is provided. Then, we use it, together with the analytic method, to derive the asymptotic expansion of the first Melnikov function near the loop. Meanwhile, we present the first coefficients in the expansion, which can be applied to study the limit cycle bifurcation near the loop. We give sufficient conditions for this system to have 14 limit cycles in the neighborhood of the loop. As an application, a piecewise polynomial Lienard system is investigated, finding six limit cycles with the help of the obtained method.

• 出版日期2016-6-15
• 单位南京信息工程大学