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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.
34A37Differential equations with impulses
37N25Dynamical systems in biology
34D05Asymptotic stability of ODE