Du, Yihong

Pang, Peter Y H

Wang, Mingxin

2008

In this paper, we propose a diffusive prey-predator model with stage structure for the predator. We first analyze the stability of the nonnegative steady states for the reduced ODE system and then study the same question for the corresponding reaction-diffusion system with homogeneous Neumann boundary conditions. We find that a Hopf bifurcation occurs in the ODE system, but no Turing pattern happens in the reaction-diffusion system. However, when a natural cross diffusion term is included in the model, we can prove the emergence of stationary patterns (i.e., nonconstant positive stationary solutions) for this system; moreover, these stationary patterns do not exist in the considered parameter regime when there is no cross diffusion.

SIAM Journal on Applied Mathematics, 69(2), p. 596-620

1095-712X

0036-1399

https://hdl.handle.net/1959.11/3690

Society for Industrial and Applied Mathematics

Quantitative analysis of a prey-predator model with stage structure for the predator

Journal Article

Publication