A dynamics research in a predator-prey system with a nonlinear growth rate. (Chinese. English summary) Zbl 1340.35156

Yang, Wenbin; Li, Yanling

J. Shandong Univ., Nat. Sci. 50, No. 3, 80-87, 94 (2015).

Summary: This paper is concerned with dynamics of a predator-prey system subject to homogeneous Dirichlet boundary conditions, where the predator population reproduces by the nonlinear function \(1/(1+ev)\). Existence and uniqueness of coexistence states for the predator-prey system are investigated. Moreover, some asymptotic behaviors of time-dependent solutions are shown and some numerical simulations are done to complement the analytical results. The main tools used here include an implicit function theorem, bifurcation theory and perturbation technique.

MSC:

35K57	Reaction-diffusion equations
92D25	Population dynamics (general)
35A01	Existence problems for PDEs: global existence, local existence, non-existence
35A02	Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness

Keywords:

reaction-diffusion equations; positive solution; uniqueness; stability; predator-prey system