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Chaos in three species food chain system with impulsive perturbations. (English) Zbl 1066.92060

Summary: We investigate a three species food chain system with periodic constant impulsive perturbations of mid-level predator. Conditions for extinction of lowest-level prey and top predator are given. By using the Floquet theory of impulsive equation and small amplitude perturbation skills, we consider the local stability of lowest-level prey and top predator eradication periodic solutions. Further, influences of the impulsive perturbations on the inherent oscillations are studied numerically, which show the rich dynamics (for example: period doubling, period halfing, non-unique dynamics) in the positive octant. The dynamical behavior is found to be very sensitive to the parameter values and initial value.

MSC:

92D40 Ecology
34A37 Ordinary differential equations with impulses
37N25 Dynamical systems in biology
34D05 Asymptotic properties of solutions to ordinary differential equations
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