Invited by Prof. Guo Lin, Prof. Sanling Yuan from College of Science, University of Shanghai for Science and Technology will give a lecture.

Title: Complex dynamics of a predator-prey system with herd and schooling behavior: with or without delay and diffusion

Time: 16:00 p.m.,Apr. 25th, 2021

Location: Room 631, Polytechnic building

Abstract: This talk is mainly about the dynamics of a predator-prey system incorporating a new type functional response function accounting for both the herd behavior for prey and the schooling behavior for predator. In the absence of spatial diffusion and time delay, we investigate the existence of extinction region and the stability of all feasible nonnegative equilibria, obtain conditions under which the system undergoes saddle-node, Hopf and Bogdanov-Takens types of bifurcations. For the spatiotemporal system, we investigate the existence of Hopf bifurcation induced by time delay near one of the positive equilibria and derive conditions for determining the property of the bifurcating periodic solution by using the normal form theory and center manifold reduction. Further, we investigate the effects of time delay or/and diffusion on the dynamics of the system, and the results show that both time delay and spatial diffusion play significant roles in determining the dynamics of the system.