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Study of stability and bifurcation of three species food chain model with non-monotone functional response. (English) Zbl 1486.92315

Summary: In this research article, we consider a tri-trophic food chain model with one prey and two predators such as- prey, intermediate predator and top predator. In this model, the prey and intermediate predator follows non-monotonic functional response; top predator consumes prey and intermediate predator following Holling type I functional response. The positivity, boundedness of solutions of the proposed model and stability conditions of different equilibrium points are discussed here. Then using center manifold theorem, the nature of non-hyperbolic type equilibrium points are discussed. After that, different local bifurcations such as saddle-node, transcritical and Hopf bifurcations are studied theoretically as well as numerically by considering half-saturation constant and death rate of intermediate predator as the bifurcation parameters. Finally, the dynamics of the proposed model has been illustrated with the help of some numerical simulations.

MSC:

92D40 Ecology
92D25 Population dynamics (general)
34D20 Stability of solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
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