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Dynamical consequences of predator interference in a tri-trophic model food chain. (English) Zbl 1181.37120
Summary: A model food chain involving a specialist and a generalist predator is proposed and studied. One of the salient features of this model food chain is that it combines both the schemes (Volterra and Leslie) of modeling predator-prey interaction in one system in such a way that the demerits of these individual formulations are suppressed and the resulting model system represents a common unit of real world food webs. The stability analysis of the proposed model is carried out. The Hopf bifurcation conditions of the positive equilibrium point are established. Our numerical computations show that chaotic dynamics is sensitive to changes in values of parameters measuring attributes of either interacting populations or their environments. Two dimensional parameter scans suggest that the model food chain displays short-term recurrent chaos. This can be regarded as a plausible explanation for why it has been so difficult to detect deterministic chaos in natural populations.

MSC:
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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