题  目：The number of limit cycles of Josephson equation

内容简介：In this talk, we will study the Josephson equations，which can be transformed the following Lienard systems on the cylinder: x’(t)=y, y’(t)=-(sin x-a)-(b+c cos x)y. We concern the non-contractible limit cycles, which are the isolated 2\pi-periodic solutions y=y(x). This problem is equivalent to study the non-zero limit cycles of the following Abel equations y’(x)=（b+cos x）y^2-(sin x-a) y^3. By the theory of rotation vectors and studying the multiplicity of limit cycles, we will show that at most two non-zero limit cycles can appear. Our work can be also viewed as a step to solve the following open problem: Open problem: y’(x)=(a_0+a_1 sin x+a_2 cos x)y^3+(b_0+b_1 sin x+b_2 cos x)y^2 have at most three limit cycles (The trivial limit cycle y=0 is included). This is a joint work with Xiangqin Yu and Hebai Chen.

报告人：刘长剑  教授

报告人简介：中山大学数学学院（珠海）教授。本、硕、博均毕业于北京大学，并获北京大学-里尔第一大学联合培养博士学位。主要从事常微分方程与动力系统方面的研究，在Trans. AMS, JDE, Nonlinearity 等杂志发表论文40余篇，主持多项国家自然科学基金面上项目。

时  间：2023年5月4日（周四）上午 10：00 始

地  点：暨南大学番禺校区 教学楼 N421

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信息科学技术学院

2023年4月28日