Limit cycle bifurcations by perturbing a class of integrable systems with a polycycle

作者：Wang, Yanqin; Han, Maoan^*

来源：Journal of Mathematical Analysis and Applications, 2014, 418(1): 357-386.

DOI：10.1016/j.jmaa.2014.03.091

• Heteroclinic loop
• Near-integrable system
• Melnikov function
• Limit cycle bifurcation

In this paper, we deal with the problem of limit cycle bifurcation near a 2-polycycle or 3-polycycle for a class of integrable systems by using the first order Melnikov function. We first get the formal expansion of the Melnikov function corresponding to the heteroclinic loop and then give some computational formulas for the first coefficients of the expansion. Based on the coefficients, we obtain a lower bound for the maximal number of limit cycles near the polycycle. As an application of our main results, we consider quadratic integrable polynomial systems, obtaining at least two limit cycles.

• 出版日期2014-10-1
• 单位常州大学; 上海师范大学