Abstract
In this paper we represent a predator-prey model in temporal as well as spatio-temporal contexts which follows Beddington-DeAngelis (simply written as BD) functional response while prey forming a square shaped herd as a form of group defense and the predator who is provided additional food with the combination of primary food to improve the absolute growth of the predator to restrain the prey population. Boundedness, local stability criterion of equilibrium points, persistence conditions, global stability conditions of interior equilibrium point, the extinction criterion for the prey and predator population, bifurcation theory at the equilibrium points of the system are elaborately investigated. The Turing instability of two species prey-predator dynamical model system is thoroughly discussed. The structural interpretation of Turing patterns are derived by weakly non-linear analysis using amplitude equations. Lastly, the diffusion of dynamical system in the spatial domain is depicted by different pattern formations. The results of theoretical analysis are well justified with numerical simulations. Thus we conduct our results in the ecosystem and yield the concept of group defence of prey and additional food to predator.
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