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

Zhang, Shuwen; Tan, Dejun; Chen, Lansun

Chaos Solitons Fractals 27, No. 3, 768-777 (2006).

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.

Reviewer: E. Ahmed (Mansoura)

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

Keywords:

impulsive; periodic solutions; Beddington-DeAngelis functional response; food chain

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