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Coexistence and partial extinction in a delay competitive system subject to impulsive harvesting and stocking. (English) Zbl 1214.34075

This paper studies the behaviour of a two-species delayed competitive system that includes impulsive harvesting and stocking.

Using technical tools from the theory of impulsive differential equations, two main issues are proposed: (a) This paper establishes sufficient conditions to guarantee the coexistence of both species. (b) A set of sufficient conditions to obtain a similar result, the competitive exclusion principle, is proposed. Under some appropiate assumptions, it is observed that the values of the delays have no influence on the coexistence or partial extinction of the model.

The paper ends with some numerical simulations to illustrate the theoretical results.

MSC:
34K60Qualitative investigation and simulation of models
34K45Functional-differential equations with impulses
34K25Asymptotic theory of functional-differential equations
92D25Population dynamics (general)