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Dynamic behaviors of the impulsive periodic multi-species predator-prey system. (English) Zbl 1165.34308
Summary: The dynamic behaviors of an impulsive periodic predator-prey model with \(n\)-preys and \(m\)-predators are studied in this paper. By constructing a suitable Lyapunov function and using the Comparison theorem of impulsive differential equation, sufficient conditions which ensure the permanence and global attractivity of the system are obtained. At the same time, a set of criteria which guarantee that some species in the system are permanent and globally attractive while the remaining species are driven to extinction is obtained. Our results show that, for the multi-species predator-prey community, impulsivity is one of the important reasons that can change the long time behaviors of species.

MSC:
34A37 Ordinary differential equations with impulses
34D05 Asymptotic properties of solutions to ordinary differential equations
92D25 Population dynamics (general)
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