报告题目1：Limit cycles and stability analysis in 3-piecewise linear differential systems with a double heteroclinic loop

报告人：刘姗姗讲师，福建师范大学

报告时间：2026年1月5日（周一）8:30

报告地点：20-308

报告摘要：This talk is devoted to studying lower and upper bounds of the number of limit cycles in a class of 3-piecewise linear differential systems with a double heteroclinic loop under perturbations of polynomials with degree n. By using the first order Melnikov function, we obtain that 2n limit cycles can appear near two centers and the double heteroclinic loop respectively, and that there are at most 2n+2[( n+1)/2]+2 limit cycles bifurcating from two period annuluses between two centers and the double heteroclinic loop up to the first order in ε. In particular, for n = 3, we consider a 3-piecewise linear Z2-equivariant system and, by using the stability-changing method, obtain a total of ten limit cycles, four of which are alien limit cycles with two large ones surrounding two symmetric smaller ones.

报告人简介：刘姗姗，福建师范大学讲师。主要从事微分方程与动力系统方向的研究工作，特别是弱化的Hilbert第16问题、同宿异宿等极限环分支问题，在J. Differential Equations、Chaos Solitons Fractals、Comput. Appl. Math.、Bull. Sci. Math. 等SCI学术期刊上发表论文多篇。

报告题目2：Bifurcations of Limit Cycles in near-Hamiltonian Systems on the Cylinder

报告人：可爱青年研究员，东华大学

报告时间：2026年1月5日（周一）8:30

报告地点：20-308

报告摘要：This presentation shows the research progress on the bifurcations of limit cycles in near-Hamiltonian systems on the cylinder. We also consider the double homoclinic bifurcation of limit cycles on the cylinder. We derive a sufficient condition for determining a lower bound of the maximum number of limit cycles near the double homoclinic loop. Furthermore, we also provide an application of our main results to a class of cylindrical systems.

报告人简介：可爱，东华大学青年研究员，博士毕业于上海师范大学，曾在浙江师范大学从事博士后工作，现主要从事微分方程与动力系统研究。在Journal of Differential Equations、Qualitative Theory of Dynamical Systems、Physica D、International Journal of Bifurcation and Chaos等国际SCI期刊发表论文多篇，主持国家自然科学基金青年项目1项（2024年1月-2026年12月）。

邀请人：动力系统与非线性分析研究所