Turing patterns in a Leslie-Gower predator prey model

TL;DR

This paper introduces a reaction-diffusion predator-prey model incorporating fear effects and prey refuge, analyzing conditions for Turing instability and pattern formation in ecological systems.

Contribution

It presents a new Leslie-Gower predator-prey model with Beddington-DeAngelis response, including fear and refuge effects, and provides stability and Turing pattern analysis.

Findings

Conditions for Turing instability are established.

Different Turing patterns emerge under various parameters.

The model demonstrates spatial population redistribution.

Abstract

A reaction-diffusion Leslie-Gower predator-prey model, incorporating the fear effect and prey refuge, with Beddington-DeAngelis functional response, is introduced. A qualitative analysis of the solutions of the model and the stability analysis of the coexistence equilibrium, are performed. Sufficient conditions guaranteeing the occurrence of Turing instability have been determined either in the case of self-diffusion or in the case of cross-diffusion. Different types of Turing patterns, representing a spatial redistribution of population in the environment, emerge for different values of the model parameters.