publication . Article . Other literature type . 2016

the long time behavior of a stochastic logistic model with infinite delay and impulsive perturbation

Lu, Chun; Wu, Kaining;
Open Access
  • Published: 01 Jul 2016 Journal: Taiwanese Journal of Mathematics, volume 20, pages 921-941 (issn: 1027-5487, Copyright policy)
  • Publisher: The Mathematical Society of the Republic of China
Abstract
This paper considers a stochastic logistic model with infinite delay and impulsive perturbation. Firstly, with the space $C_{g}$ as phase space, the definition of solution to a stochastic functional differential equation with infinite delay and impulsive perturbation is established. According to this definition, we show that our model has an unique global positive solution. Then we establish the sufficient and necessary conditions for extinction and stochastic permanence of the model. In addition, the effects of impulsive perturbation and delay on extinction and stochastic permanence are discussed, respectively.
Subjects
free text keywords: Mathematical analysis, Mathematics, Perturbation (astronomy), Logistic regression, Extinction, Phase space, Functional differential equation, White noise, impulsive perturbation, stochastic permanence, infinite delay, 60H40, 92B05, 69N25
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publication . Article . Other literature type . 2016

the long time behavior of a stochastic logistic model with infinite delay and impulsive perturbation

Lu, Chun; Wu, Kaining;