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| In this paper, we study a strongly coupled
reaction-diffusion system describing three interacting species in a
food chain model, where the third species preys on the second one
and simultaneously the second species preys on the first one. We
first show that the model is very rich dynamically. We conduct a one parameter analysis which illustrate the existence of chaos, limit cycle, and stable equilibrium while the parameter changes. Some interesting dynamical phenomena occur when we perform analysis of interactions in term of self-production of prey and self-competition of the middle predator. Then we conduct linear stability analysis and various phenomena exist such as Turing instability, as well as diffusion induced chaos. By numerical simulations,it shows the existence of various patterns such as stripe pattern, spot pattern, and labyrinth patterns. |
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