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

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.