Emergent impacts of quadratic mortality on pattern formation in a predator–prey system

Abstract

In this paper, we have investigated the effects of spatial diffusion in the pattern formation of a predator–prey system with quadratic mortality rate of the predator in the presence of habitat complexity. Using linear stability analysis, the regions of parameter space are plotted, and several kinds of instability regions are identified. Special attention has been given to investigate the selection of spatio-temporal patterns in the neighborhood of a critical parameter using the amplitude equation formalism. Choosing control parameter from the Turing space, the existence conditions for stable patterns are derived using the amplitude equations. Results obtained from theoretical analysis of amplitude equations agree very well with the numerical simulation results near the critical parameter value. Numerical simulations are done to show the existence of different spatio-temporal patterns. Spiral patterns are obtained in the suitable parameter region. It is shown that varying only the death rate of the predator, the spatio-temporal chaos can be controlled. Our investigations show that patterns are sensitive to the variation of habitat complexity and death rate of predator and patterns can be controlled by tuning the death rate of the predator.