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**Analysis of a stochastic Lotka-Volterra competitive model with infinite delay and impulsive perturbations.**
*(English)*
Zbl 1390.34232

Summary: This paper considers a stochastic Lotka-Volterra competitive model with infinite delay and impulsive perturbations. This model is new, more feasible and more accordance with the actual. The aim is to analyze what happens under the impulsive perturbations. With space \(C_{g}\) as phase space, sufficient conditions for permanence in time average are established as well as extinction, stability in time average and global attractivity of each population. Numerical simulations are also exhibited to illustrate the validity of the results in this paper. In addition, a knowledge is given to illustrate that the statement in [Q. Liu and Q. Chen, J. Math. Anal. Appl. 433, No. 1, 95–120 (2016; Zbl 1326.92060)] is incorrect by choosing space \(C_{g}\) as phase space. Our results demonstrate that impulsive perturbations which may represent human factor play a key role in protecting the population when environmental noise and interaction rates are disadvantageous to population survival.

### MSC:

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

34K45 | Functional-differential equations with impulses |

34K50 | Stochastic functional-differential equations |

34K25 | Asymptotic theory of functional-differential equations |

34K20 | Stability theory of functional-differential equations |

92D25 | Population dynamics (general) |

### Keywords:

impulsive perturbations; environmental noise; infinite delay; permanence in time average; stability### Citations:

Zbl 1326.92060
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\textit{C. Lu} and \textit{Q. Ma}, Taiwanese J. Math. 21, No. 6, 1413--1436 (2017; Zbl 1390.34232)

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