Spatiotemporal pattern formation in a prey-predator model under environmental driving forces

TL;DR

This study investigates how environmental noise influences pattern formation in a predator-prey reaction-diffusion model, revealing new spatial patterns outside traditional Turing instability conditions through numerical simulations.

Contribution

It introduces a stochastic predator-prey model with environmental noise and analyzes the resulting spatiotemporal patterns beyond classical Turing theory.

Findings

Noise induces spatial patterns outside Turing regions

Patterns depend on noise intensity and system parameters

Numerical simulations characterize Turing and Turing-Hopf patterns

Abstract

Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this paper, we focus on the spatiotemporal patterns produced by the predator-prey model with ratio-dependent functional response and density dependent death rate of predator. We get the reaction-diffusion equations incorporating the self-diffusion terms, corresponding to random movement of the individuals within two dimensional habitats, into the growth equations for the prey and predator population. In order to have to have the noise added model, small amplitude heterogeneous perturbations to the linear intrinsic growth rates are introduced using uncorrelated Gaussian white noise terms. For the noise added system, we then observe spatial patterns for the parameter values lying outside the Turing instability region. With thorough numerical simulations we characterize the patterns corresponding to Turing and Turing-Hopf domain and study their dependence on different system parameters like noise-intensity, etc.