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

Authors

  • O.D. Borysenko Taras Shevchenko National University of Kyiv
  • D.O. Borysenko Taras Shevchenko National University of Kyiv

DOI:

https://doi.org/10.17721/1812-5409.2019/1.1

Abstract

It is investigated the non-autonomous logistic differential 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 dierential equation, stochastic differential equation, centered and non-centered Poisson measures.

Pages of the article in the issue: 10-13

Language of the article: Ukrainian

References

IANNELLi, M. and PUGLIESE, A. (2014), An Introduction to Mathematical Population Dynamics, Springer, 351 p.

LIU, MENG and WANGA, KE (2011) Persistence and extinction in stochastic nonautonomous logistic systems", Journal of Mathematical Analysis and Applications, 375, 443-457.

BORYSENKO, O.D. and BORYSENKO, D.O. (2017), Non-autonomous stochastic logistic dierential equation with non-centered Poisson measure, Bulletin of Taras Shevchenko National University of Kyiv, Series: Physics & Mathematics, (2017), no.4, 9-14.

BORYSENKO, O.D. and BORYSENKO, D.O. (2018) Persistence and extinction in stochastic nonautonomous logistic model of population dynamics, Theory of Probability and Mathematical Statistics, no.2(99), 63-70.

GIKHMAN, I.I. and SKOROKHOD, A.V. (1982), Stochastic Differential Equations and their Applications, Naukova Dumka, Kiev, 611p. (in Russian)

BORYSENKO, O.D. and BORYSENKO, D.O. (2019), Asymptotic behavior of solution to the non-autonomous stochastic logistic differential equation, Theory of Probability and Mathematical Statistics, n.2(101), 55-64.

No 1 (2019)

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How to Cite

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

Issue

No. 1 (2019)

Section

Algebra, Geometry and Probability Theory

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