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Impulsive perturbations of a three-trophic prey-dependent food chain system
Authors:Paul Georgescu  Gheorghe Moroanu
Institution:aDepartment of Mathematics, Technical University of Iaşi, Bd. Copou 11, 700506 Iaşi, Romania;bDepartment of Mathematics and its Applications, Central European University, Nador u. 9, 1051 Budapest, Hungary
Abstract:The dynamics of an impulsively controlled three-trophic food chain system with general nonlinear functional responses for the intermediate consumer and the top predator are analyzed using the Floquet theory and comparison techniques. It is assumed that the impulsive controls act in a periodic fashion, the constant impulse (the biological control) and the proportional impulses (the chemical controls) acting with the same period, but not simultaneously. Sufficient conditions for the global stability of resource and intermediate consumer-free periodic solution and of the intermediate consumer-free periodic solution are established, the latter corresponding to the success of the integrated pest management strategy from which our food chain system arises. In this regard, it is seen that, theoretically speaking, the control strategy can be always made to succeed globally if proper pesticides are employed, while as far as the biological control is concerned, its global effectiveness can also be reached provided that the top predator is voracious enough or the (constant) number of top predators released each time is large enough or the release period is small enough. Some situations which lead to chaotic behavior of the system are also investigated by means of numerical simulations.
Keywords:Simple food chain  Integrated pest management  Impulsive perturbations  Global stability  Chaos
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