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Complex dynamics of a three species food-chain model with Holling type IV functional response. (English) Zbl 1272.49085
Summary: In this paper, dynamical complexities of a three species food chain model with Holling type IV predator response is investigated analytically as well as numerically. The local and global stability analysis is carried out. A persistence criterion of the food chain model is obtained. Numerical bifurcation analysis reveals the chaotic behavior in a narrow region of the bifurcation parameter space for biologically realistic parameter values of the model system. Transition to chaotic behavior is established via period-doubling bifurcation and some sequences of distinctive period-halving bifurcation leading to limit cycles are observed.

MSC:
49N75 Pursuit and evasion games
93A30 Mathematical modelling of systems (MSC2010)
49K40 Sensitivity, stability, well-posedness
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