Stochastic permanence of solution to stochastic non-autonomous logistic equation with jumps

Borysenko, O., Borysenko, D. (2019). Stochastic permanence of solution to stochastic non-autonomous logistic equation with jumps. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(1), 10–13. https://doi.org/10.17721/1812-5409.2019/1.1

It is investigated the non-autonomous logistic dierential equation with disturbance of coeffcients by white noise, centered and non-centered Poisson noises. The coeffcients of equation are locally Lipschitz continuous but do not satisfy the linear growth condition. This equation describes the dynamics of population in the Verhulst model which takes into account the logistic eect: an increase of the population size produces a fertility decrease and a mortality increase; since resources are limited, if the population size exceeds some threshold level, the habitat cannot support the growth. The property of stochastic permanence is desirable since it means the long time survival in a population dynamics. The suffcient conditions for the stochastic permanence of population in the considered model is obtained.Key words: stochastic permanence, non-autonomous logistic differential equation, stochastic differential equation, centered and non-centered Poisson measures.Pages of the article in the issue: 10 - 13Language of the article: Ukrainian