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Impulsive perturbations in a periodic delay differential equation model of plankton allelopathy. (English) Zbl 1190.34084

Authors’ abstract: This paper studies the dynamics of a periodic impulsive delay two-species competitive system of plankton allelopathy. If the impulsive perturbations and the intrinsic growth rates are relatively large while the interspecific competing rates are relatively small, then the system is permanent. If impulsive perturbations and the intrinsic growth rates are relatively small, then the two species tend toward extinction. The impulsive perturbations have effect on existence of positive periodic solutions for the system. The effect of toxic substances is harmless for such solutions. Under appropriate assumptions, delays have no effect on the permanence, extinction and existence of positive periodic solutions for the system.

MSC:

34K13 Periodic solutions to functional-differential equations
34K45 Functional-differential equations with impulses
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D25 Population dynamics (general)
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