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Dynamical behavior of a three species food chain model with Beddington-DeAngelis functional response. (English) Zbl 1195.92061

Summary: A three species food chain model with Beddington-DeAngelis functional response is investigated. A local stability analysis is carried out and the global behavior is simulated numerically for a biologically feasible choice of the parameters. Persistence conditions for the food chain model are established. Bifurcation diagrams are obtained for different parameters of the model after intensive numerical simulations. The results of simulations show that the model could exhibit chaotic dynamics for realistic and biologically feasible parameter values. Finally, the effect of immigration of the prey species is investigated. It is observed that adding a small amount of constant immigration to the prey species stabilizes the system.

MSC:

92D40 Ecology
65C20 Probabilistic models, generic numerical methods in probability and statistics
34C60 Qualitative investigation and simulation of ordinary differential equation models
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34D20 Stability of solutions to ordinary differential equations
37N25 Dynamical systems in biology
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References:

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