Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

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In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered.The conditions for the onset of cross-diffusion-driven instability are obtained by linear stability analysis.The technique of multiple time scales Gear Bags is employed to deduce the amplitude Sand Filter equation near Turing bifurcation threshold by choosing the cross-diffusion coefficient as a bifurcation parameter.The stability analysis of these amplitude equations leads to the identification of various Turing patterns driven by the cross-diffusion, which are also investigated through numerical simulations.