Turing patterns in a diffusive Holling-Tanner predator-prey model with an alternative food source for the predator

TL;DR

This paper investigates Turing pattern formation in a modified Holling-Tanner predator-prey model with alternative food sources, analyzing conditions for instability and illustrating spatio-temporal patterns through simulations.

Contribution

It introduces a modified predator-prey model incorporating alternative food sources and analyzes the conditions for Turing instability and pattern formation.

Findings

Identification of parameter regions with Turing instability

Numerical evidence of spatio-temporal periodic solutions

Simulation results illustrating pattern dynamics

Abstract

In this manuscript, we consider temporal and spatio-temporal modified Holling-Tanner predator-prey models with predator-prey growth rate as a logistic type, Holling type II functional response and alternative food sources for the predator. From our result of the temporal model, we identify regions in parameter space in which Turing instability in the spatio-temporal model is expected and we show numerical evidence where the Turing instability leads to spatio-temporal periodic solutions. Subsequently, we analyse these instabilities. We use simulations to illustrate the behaviour of both the temporal and spatio-temporal model.