Stationary Patterns of a Cross-Diffusion Prey-Predator Model with Holling Type II Functional Response

Author:

Zhang Hongtao1ORCID,Zhao Jingfu1

Affiliation:

1. School of Mathematics and Information Science, Zhongyuan University of Technology, Zhengzhou 450007, China

Abstract

In this paper, we consider positive steady-state solutions of a cross-diffusions prey-predator model with Holling type II functional response. We investigate sufficient conditions for the existence and the nonexistence of nonconstant positive steady state solutions. It is observed that nonconstant positive steady states do not exist with small cross-diffusion coefficients, and the constant positive steady state is global asymptotically stable without cross-diffusion. Furthermore, we show that if natural diffusion coefficient or cross-diffusion coefficient of the predator is large enough and other diffusion coefficients are fixed, then under some conditions, at least one nonconstant positive steady state exists.

Funder

Zhongyuan University of Technology

Publisher

Hindawi Limited

Subject

General Mathematics

Reference23 articles.

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