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.
Naveed Iqbal, Ranchao Wu. (2019) Phase transition induced by noise in a predator–prey model with herd behavior, Punjab University Journal of Mathematics, Volume 51, Issue 12.
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