Stabilizing Role of Nonlocal Interaction on Spatio-temporal Pattern Formation

¹ Department of Mathematics & Statistics, IIT Kanpur, Kanpur, INDIA
² Department of Mathematics and Mathematical Statistics, Umea University, Umea, Sweden

^* Corresponding author. E-mail: malayb@iitk.ac.in

Abstract

Here we study a spatio-temporal prey-predator model with ratio-dependent functional response and nonlocal interaction term in the prey growth. For a clear understanding of the effect of nonlocal interaction on the resulting stationary and non-stationary patterns, we consider the nonlocal interaction term in prey growth only to describe the nonlocal intra-specific competition due to limited resources for the prey. First we obtain the patterns exhibited by the basic model in the absence of nonlocal interaction and then explore the effect of nonlocal interaction on the resulting patterns. We demonstrate the stabilizing role of nonlocal interaction as it induces stationary pattern from periodic and chaotic regimes with an increase in the range of nonlocal interaction. The existence of multiple branches of stationary solutions, bifurcating from homogeneous steady-state as well as non-stationary patterns, is illustrated with the help of numerical continuation technique.