报告1 ：Complex dynamics of a SIRS epidemic model with the influence of hospital bed number

  时 间：2021年1月4日19：00-19：50      

  地  点：  腾讯会议（ID： 127 649 138）

In this talk, the nonlinear dynamics of a SIRS epidemic model with vertical transmission rate of neonates, nonlinear incidence rate and nonlinear recovery rate are investigated. We focus on the influence of public available resources (especially the number of hospital beds) on disease control and transmission. The existence and stability of equilibria are analyzed with the basic reproduction number as the threshold value. The conditions for the existence of transcritical bifurcation, Hopf bifurcation, saddle-node bifurcation, backward bifurcation and the normal form of Bogdanov-Takens bifurcation are obtained. In particular, the coexistence of limit cycle and homoclinic cycle, and the coexistence of stable limit cycle and unstable limit cycle are also obtained. This study indicates that maintaining enough number of hospital beds is very crucial to the control of the infectious diseases no matter whether the immunity loss population are involved or not. Finally, numerical simulations are also given to illustrate the theoretical results.

报告2：Overexploitation occurs in the Rosenzweig-MacArthur model with trigonometric functional response

时 间：2021年1月4日19:50-20：40    

地  点：  腾讯会议ID： 127 649 138

In this talk, we study a Rosenzweig-MacArthur predator-prey system with a strong Allee effect, and take a predator functional response to the hyperbolic tangent form as trigonometric. We study both the local and global dynamics, and the possible bifurcation is determined according to the variation of the carrying capacity of the prey. An analytic expression is given to determine the criticality of Hopf bifurcation, and the resulting Hopf bifurcation is proved to be supercritical or subcritical. The existence of heteroclinic orbit and Bautin bifurcation are also proved. Biologically speaking, such a heteroclinic cycle always forms a boundary of the region in two parameter space which indicates the breakdown of the system after the invasion of the predator, i.e., overexploitation occurs. Further, numerical simulations are given to demonstrate the theoretical results which include the coexistence of limit cycles and heteroclinic cycles.

报告3：The role of intraspecific competition and prey refuge in Rosenzweig-MacArthur model

时 间：2021年1月4日20:40-21：30    

地  点：  腾讯会议ID： 127 649 138

 

In this talk, we study a Rosenzweig-MacArthur predator-prey model with intraspecific competitions of predators, and take a predator functional response to Holling type II form with a refuge protecting of the prey by using the dynamical approach. We study the number of positive equilibria, the local and global dynamics

including Hopf bifurcation, saddle-node bifurcation, Bautin bifurcation and Bogdanov-

Takens bifurcation. In addition, the coexistence of stable limit cycles and unstable limit

cycles is also given. Particularly, the hydra effect is found which describes the positive

effect of the death rate of predators having on the population abundance, and the

positive effects of prey refuge, intraspecific competition among predators are also

found, which are similar to the hydra effect caused by the death rate of predators. The

bistability or Allee effect are not necessary conditions for the occurrence of multiple

hydra effect. Further, numerical simulations are used to demonstrate the theoretical

results including the existence of the hydra effect region and trophic cascade. Finally, some conclusions and discussions are given.

徐衍聪教授简介：杭州师范大学教授,硕士生导师,美国（SIAM）工业与应用数学会员,美国数学评论评论员。先后访问美国布朗大学、日本京都大学、德国不莱梅大学等高校。目前主要从事动力系统分支理论、局部结构分支及应用研究,主要包括：Dynamical Systems,Dynamics of Patterns, Nonlinear Wave,Homoclinic and Heteroclinic Phenomena等研究工作。主持国家自然科学基金面上项目、浙江省自然科学基金、日本GCOE项目及参与各类基金10余项。