This talk concerns with the reaction-diffusion systems modeling the population dynamics of two predators and one prey with nonlinear prey-taxis. We first investigate the global existence and boundedness of the unique classical solution for the general model. Then we study the global stabilities of nonnegative spatially homogeneous equilibria for an explicit system with type I functional responses and density-dependent death rates for the predators and logistic growth for the prey. Moreover, the convergence rates are also established.
Mingxin Wang, Ph.D. and Professor, Natural Science Research Center, Harbin Institute of Technology. His main research interests are existence and uniqueness, regularity, global existence and finite time blow-up, asymptotic behavior, steady state solutions, bifurcation and stability, travelling waves, free boundary problems coming from ecology and epidemiology, boundary blow-up problems in the Nonlinear Parabolic and Elliptic Equations.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai