报告题目：Predicting the global bifurcation dynamics of a SIRS disease model

报 告 人：徐衍聪教授（中国计量大学）

时    间：2024年4月8日 16:30-17:30

地   点：数学楼301会议室

摘  要：In this paper, the global dynamics of a susceptible infectious recovered (SIRS) epidemic model with a generalized non-linear incidence function are investigated. It is shown that (1) not the basic reproduction number, but a sub-threshold value acts as a threshold value for the disease spread; (2) as parameters vary, the model exhibits saddle-node bifurcation, forward bifurcation, backward bifurcation, cusp type degenerate Bogdanov-Takens bifurcation of codimension 2 and 3, Hopf bifurcation, generalized Hopf bifurcation, homoclinic bifurcation, degenerate homoclinic bifurcation. Particularly, we find the existence of isolas of limit cycles, which tells us that two stable limit cycles and one unstable limit cycles coexist. We derive that the existence of codimension-three Bogdanov-Takens bifurcation as the organizing center of complex dynamics yields the bifurcation of homoclinic cycle and isola bifurcation of limit cycles, which provide the possible existence of three limit cycles. Actually, two limit cycles can emanate simultaneously from the isola center. Numerical simulations are presented to illustrate the theoretical results.

报告人简介：

徐衍聪，中国计量大学理学院教授，博士生导师，华东师范大学应用数学专业博士，浙江大学博士后，美国工业与应用数学学会会员，美国数学会会员，浙江省数理医学会理事，浙江省ZSMM生物医学数学专业委员会主任，曾入选浙江省优秀中青年骨干教师，杭州市优秀教师，校优秀中青年支持计划，校教学十佳，校十佳班主任等。先后访问美国布朗大学，德国不莱梅大学，日本京都大学，加拿大约克大学等高校。先后主持国家自然科学基金面上项目、天元基金、日本全球卓越中心（GCOE）项目，归国留学基金、博士后基金、浙江省自然科学基金等。主要从事动力系统分支理论及应用研究。