Investigating the role of fear and top predator interference on the spatio-temporal dynamics of food chain model
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Abstract
In this paper, attempt has been made to grasp the idea about the role of fear effect of intermediate specialist predator on prey and the effect of the top predator interference in the spatial framework of a three species food chain model. By introducing a hybrid model and assuming that the interaction between prey and intermediate predator obeys the Volterra scheme, whereas Beddington-DeAngelis (BD) type functional response is taken in between the top predator and its favorite food. The stability properties of each equilibrium point of the temporal model system, blow up in finite time for both temporal and spatial systems corresponding to a large initial data are established. We pay attention to illustrate different types of patterns around the neighbourhood of a critical parameter. Choosing appropriate control parameter from the Turing space and using the existence criteria, stable patterns are obtained. The result of theoretical analysis well agrees with the result exhibited through numerical simulations around the critical parameter. Finally, numerical simulation illustrates the role of diffusion in the spatial domain by formations of different patterns.
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