Pattern Formation in a Prey-Predator Model with Nonlocal Interaction Terms

Stabilizing Role of Nonlocal Interaction on Spatio-temporal Pattern Formation

“…d) is small. Recently we have proved the stabilizing role of nonlocal interaction term leading to stationary patterns over a large range of parameter values [5]. We have also established the existence of multiple stationary branches of solution implying the extension of stationary patch sizes as an evolutionary behavior.…”

“…It means that prey individuals can move from one location to another for the consumption of resources and hence compete with the prey individuals present at those location as well coming from nearby locations also. Recently we have worked on a similar model with nonlocal interaction terms in both the population and have reported the stabilizing role of nonlocal interaction and existence of multiple stationary branches only [5]. In another work we have demonstrated the generation of Turing patterns for Rosenzweig-Macarthur model in the presence of nonlocal interaction [7].…”

“…Increase in the range of nonlocal interaction results in the overlap of nearby foraging areas and hence alters the size of the localized patches. This phenomena is responsible for the existence of multiple stationary patterns obtained through numerical continuations [5,6]. With the advancement of time individuals of the prey species can attempt to extend their range of nonlocal movement to have access to the resources lying just outside of the established patches and this ecological phenomenon results in the transition from one branch of stationary solution to the other branch.…”