Complex dynamics of a tumor-immune system with antigenicity

发布时间：2021-12-10 作者：浏览次数：

Speaker:	陈玉明	DateTime:	2021年12月16日（周四）上午8:30-9:30
Brief Introduction to Speaker: 陈玉明教授，加拿大罗瑞尔大学 (Wilfrid Laurier University)		Place:	腾讯会议：359295679
Abstract:Taking into account the effect of antigenicity, we propose and analyze a conceptual model for differential equations. Though simple, the model can have complicated dynamical behaviors. Besides the tumor-free equilibrium, there can be at most three tumor-present equilibria. The tumor-present equilibrium can be a saddle or stable node/focus. Sufficient conditions on the nonexistence of nonconstant periodic solutions are provided. Bifurcation analysis including Hopf bifurcation and Bogdanov-Takens bifurcation is carried out. The theoretical results are supported by numerical simulations. Numerical simulations reveal the complexity of the dynamical behaviors of the model, which includes the subcritical/supercritical Hopf bifurcation, homoclinic bifurcation, saddle-node bifurcation at a nonhyperbolic periodic orbit, the appearance of two limit cycles with a singular closed orbit, and so on. Some biological implications of the theoretical results and numerical simulations are also provided.