## Dynamic complexities of a food chain model with impulsive perturbations and Beddington-DeAngelis functional response.(English)Zbl 1094.34031

A 3-trophic level food chain with periodic impulsive perturbations and Beddington-DeAngelis functional response is investigated. Conditions for extinction of the top predator are given. Boundedness and persistence of solutions are studied. The influence of both the impulsive perturbation $$p$$ and its period $$T$$ is studied numerically. As $$p$$ increases ($$T$$ fixed), the solution behavior changes from limit cycle via quasi-periodic to periodic. While as $$T$$ increases ($$p$$ fixed), the solution behavior changes from periodic via a cascade of period doubling bifurcations to chaos.

### MSC:

 34C60 Qualitative investigation and simulation of ordinary differential equation models 34C23 Bifurcation theory for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations 34C28 Complex behavior and chaotic systems of ordinary differential equations 34A37 Ordinary differential equations with impulses 92D25 Population dynamics (general) 34D05 Asymptotic properties of solutions to ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations
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### References:

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