Nonexistence of nonconstant positive steady states of a diffusive predator-prey model

Shanshan Chen

doi:10.3934/cpaa.2018026

Article Contents

2018, Volume 17, Issue 2: 477-485. Doi: 10.3934/cpaa.2018026

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Nonexistence of nonconstant positive steady states of a diffusive predator-prey model

Shanshan Chen

Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong, 264209, China

Received: December 31, 2016

Revised: August 31, 2017

Published: June 2018

The authors are supported by the National Natural Science Foundation of China (No.11771109).

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Abstract

In this paper, we investigate a diffusive predator-prey model with a general predator functional response. We show that there exist no nonconstant positive steady states when the interaction between the predator and prey is strong. This result implies that the global bifurcating branches of steady state solutions are bounded loops for a predator-prey model with Holling type Ⅲ functional response.

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Mathematics Subject Classification: Primary:35K57;Secondary:35B36.

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