Pattern formation study of Hassell-Varley prey-predator system with fear effect

Abstract

The pattern formation study of diffusion model provides an idea of how the species are distributed in spatial domain. In the present work, we study the effect of fear on the formation of Turing patterns in a reaction-diffusion system. First, for a temporal system, we present existence and stability results of the positive equilibrium point. Then we prove Turing instability in a spatiotemporal system to study the pattern formation of the model due to the fear effect. Turing instability conditions ensure the existence of Turing patterns. Numerical simulation is performed to observe the effect of fear factor on system dynamics and pattern formation. In the absence of fear, Turing instability not seen in the spatiotemporal system, when terrestrial and aquatic predators form fixed number of tight groups. However, Turing instability is possible for most realistic prey-predator systems, even in the absence of fear. Round floral, square floral, regular spiral, microspiral and tubular patterns are obtained. This study shows that the interaction between diffusion and fear effect may give rise to rich dynamics in ecological systems.