Speaker：Dr. Haiyang Jin, South China University of Technology

Title: Global stability of the  prey-taxis systems 

Time: 2016-09-29, 16:00-17:00pm

Venue: Room 316 of Environment Building, Renmin University

Abstract: 

 In this talk, we prove the global boundedness and stability of the predator-prey system with prey-taxis in a two-dimensional bounded domain with Neumman boundary conditions. By deriving an entropy-like equality and the boundedness criterion,  we show that the intrinsic interaction between predators and preys is sufficient to prevent the population overcrowding even the prey-taxis is included and strong. Furthermore, by constructing appropriate Lyapunov functionals,  we show that prey-only steady state is globally asymptotically stable if the predation is weak, and the co-existence steady state is  globally asymptotically stable under some conditions (like the prey-taxis is weak or the prey diffuses fast) if the predation is strong. We also discuss the applications of the model on the biological control. This is a joint work with Prof. Zhi-An Wang.