Stationary Pattern and Global Bifurcation for a Predator–Prey Model with Prey-Taxis and General Class of Functional Responses

Author:

Maimaiti Yimamu1,Zhang Wang2,Muhammadhaji Ahmadjan13ORCID

Affiliation:

1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China

2. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, China

3. The Key Laboratory of Applied Mathematics of Xinjiang Uygur Autonomous Region, Xinjiang University, Urumqi 830017, China

Abstract

This paper will explore a predator–prey model that incorporates prey-taxis and a general functional response in a bounded domain. Firstly, we will examine the stability and pattern formation of both local and nonlocal models. Our main finding is that the inclusion of nonlocal terms enhances linear stability, and the system can generate patterns due to the effects of prey-taxis. Secondly, we consider the nonlinear prey-taxis as the bifurcation parameter in order to analyze the global bifurcation of this model. Specifically, we identify a branch of nonconstant solutions that emerges from the positive constant solution when the prey-tactic sensitivity is repulsive. Finally, we will validate the effectiveness of the theoretical conclusions using numerical simulation methods.

Funder

Talent Project of Tianchi Doctoral Program in Xinjiang Uygur Autonomous Region

National Natural Science Foundation of China

the National Natural Science Foundation of Xinjiang

the Open Project of Key Laboratory of Applied Mathematics of Xinjiang Uygur Autonomous Region

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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