Limit cycles produced near cubic homoclinic loops in near-Hamiltonian systems

发布时间：2024-09-09 作者：浏览次数：

Speaker:	田云	DateTime:	2024年9月12日（周四）上午10:30-11:30
Brief Introduction to Speaker: 上海师范大学数理学院教授，博士生导师，博士毕业于加拿大西安大略大学应用数学系，从事常微分方程定性理论、计算机符号计算和传染病模型等方向的研究，特别关注弱化的Hilbert第16问题、同宿异宿极限环分支和规范型的符号计算等相关问题。近年来，在JDE、Commun. Nonl. Sci. Numer. Simul和Nonlinear Anal. RWA等本领域主流期刊发表学术三十余篇论文。		Place:	腾讯会议：783-216-563
Abstract:In this talk, we use (high-order) Melnikov functions to study bifurcations of limit cycles around homoclinic and heteroclinic loops in near-Hamiltonian systems with small perturbations. An algorithm is constructed for the computation of the coefficients of the corresponding expansion of the first order Melnikov functions. New lower bounds are obtained for the number of limit cycles produced around homolinic and heterclinic loops in planar cubic systems.