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A periodic predator-prey-chain system with impulsive perturbation. (English) Zbl 1159.34327

Summary: A periodic predator-prey-chain system with impulsive effects is considered. By using the global results of Rabinowitz and standard techniques of bifurcation theory, the existence of its trivial, semi-trivial and nontrivial positive periodic solutions is obtained. It is shown that the nontrivial positive periodic solution for such a system may be bifurcated from an unstable semi-trivial periodic solution. Furthermore, the stability of these periodic solutions is studied.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34A37 Ordinary differential equations with impulses
92D25 Population dynamics (general)
34C23 Bifurcation theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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