A mathematical model is proposed to study a three species food web model of preypredator system in spatiotemporal domain. In this model, we have included three state variables, namely, one prey and two first order predators population with Beddington-DeAngelis predation functional response. We have obtained the local stability conditions for interior equilibrium and the existence of Hopf-bifurcation with respect to the mutual interference of predator as bifurcation parameter for the temporal system. We mainly focus on spatiotemporal system and provided an analytical and numerical explanation for understanding the diffusion driven instability condition. The different types of spatial patterns with respect to different time steps and diffusion coefficients are obtained. Furthermore, the higher-order stability analysis of the spatiotemporal domain is explored.
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