Analytical detection of stationary Turing pattern in a predator-prey system with generalist predator

Abstract

A prey-predator model with prey dependent Holling type-II functional response and a generalist predator exhibits complex dynamics in response to parameter variation. Generalist predators implicitly exploiting multiple food resources reduce predation pressure on their focal prey species that causes it to become more stable compared to a prey-predator system with specialist predator. In the temporal system, bistability and tristability are observed along with various global and local bifurcations. Existence of homogeneous and heterogeneous positive steady state solutions are shown to exist for suitable ranges of parameter values in the spatiotemporal diffusive system. Weakly nonlinear analysis using multi-scale perturbation technique is employed to derive amplitude equation for the stationary patterns near the Turing bifurcation threshold. The analytical results of the amplitude equations are validated using numerical simulations. We also identify bifurcation of multiple stable stationary patch solutions as well as dynamic pattern solution for parameter values in the Turing and Turing-Hopf regions.