Phase transition induced by noise in a predator–prey model with herd behavior

Abstract

In this article, we explore the effect of noise on pattern emergence in a predator–prey model with herd behavior developed because of stochastic partial differential equations (SPDEs). Under specific level of noise, the system is practically observed twice phase transitions. The multi–scaling approach is extended from single to multiple SPDEs. Dynamical analysis of amplitude equation interprets the structural transitions. Then we find the necessary and sufficient constraint which shows the phenomena of transition from a spacial homogenous state to spatial travelling wave. Noise has an undermining impact on the dynamics of a population by the emergence of the Hopf bifurcation. Finally, theoretical results are illustrated via numerical simulations.