报告题目：Saddle-node Bifurcation and Bogdanov-Takens Bifurcation of a SIRS Epidemic Model with Nonlinear Incidence Rate

报告人：赵育林教授，中山大学

报告时间：2024年4月29日（周一）9:30-10:30

报告地点：20-404（第一会议室）

报告摘要：The Bogdanov-Takens bifurcation of the SIRS epidemic model with nonlinear incidence rate was studied by Ruan and Wang [{J. Differential Equations, 188 (2003)], Tang, Huang, Ruan and Zhang [SIAM J. APPL. MATH., 69 (2008), pp] and Lu, Huang, Ruan and Yu [J. Differential Equations, 267 (2019)] in recent years. The results in the mentioned papers showed that the SIRS epidemic model with nonlinear incidence rate can undergo a Bogdanov-Takens bifurcation of codimension two. In this paper we study the SIRS epidemic model with nonlinear incidence rate  for general p and q. The bifurcation analysis indicates that there is a saddle-node or a cusp of codimension two for various parameter values and the model can undergo a saddle-node bifurcation or a Bogdanov-Takens bifurcation of codimension two if suitable bifurcation parameters are selected. It means that there are some SIRS epidemic model which has a limit cycle or a homoclinic loop. Moreover, it is also shown that the codimension of Bogdanov-Takens bifurcation is at most two.

报告人简介：赵育林，男，陕西省合阳县人，中山大学数学学院（珠海）院长、教授、博士生导师，广东省数学会常务理事。获2019年度广东省自然科学奖二等奖。1998年毕业于北京大学，获理学博士学位；1998年至今在中山大学工作。曾先后访问意大利佛罗伦萨大学、加拿大Universite des Montreal及York University、以色列Weizmann Institute of Science、巴西圣保罗大学、美国普渡大学、西班牙Universitat Autonoma de Barcelona等高校。主要从事常微分方程定性理论和分支理论的研究工作，包括弱化的Hilbert十六问题、周期单调性、代数极限环、高阶极限环分支问题等，已在J. Differential Equation、Nonlinearity、中国科学（英文版）等期刊上发表七十余篇学术论文，主持国家自然科学基金项目6项、教育部博士点学科基金1项、教育部留学回国人员科研启动基金1项。