题目：Limit cycles in the perturbation of a piecewise cubic quasi-homogeneous system with a global center

内容简介：In this talk we study the quasi-homogeneous center problem and the bifurcation of limit cycles in piecewise smooth differential systems. Using the higher-order Poincare Lyapunov method it presents the explicit conditions for piecewise quasi-homogeneous cubic polynomial systems that exhibit a global center. Base on one of the center conditions, it proves that such piecewise system has at least 5 limit cycles bifurcating from the quasi-homogeneous global center. Moreover, by taking advantage of the inherent structure of this piecewise quasi-homogeneous cubic system, our result provides a general expression of its first-order Melnikov function under polynomial perturbations of degree n.  Then it is utilized to determine that the Poincare cyclicity is given by  in the piecewise smooth case, and n-1 in the smooth one. These findings serve to update and generalize existing results.

报告人：陈挺

报告人简介：副教授，硕士生导师，博士毕业于湖南大学，曾在国防科技大学和巴塞罗那自治大学从事博士后和访问工作。研究方向为微分方程理论及其应用，主要包括Hilbert第16问题、中心-焦点问题、Hopf分岔、Poincaré分岔、临界周期分岔和全局结构等问题，在中国科学、J. Differential Equations、Commun. Nonlinear Sci. Number. Simulat.和Nonlinear Dynamics等本领域主流期刊发表20余篇学术论文。主持国家自然科学基金、广东省自然科学基金和国家资助博士后研究人员计划等项目。

时  间：2025年6月11日（周三）下午14：00开始

地  点：腾讯会议 450-909-757

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信息科学技术学院

2025年6月5日