Extinction and persistence in stochastic predator population density-dependent predator-prey model with jumps

Authors

  • O. D. Borysenko Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-6670-8605
  • O. V. Borysenko National Technical University of Ukraine "KPI", Kyiv

DOI:

https://doi.org/10.17721/1812-5409.2023/1.4

Keywords:

stochastic predator-prey model, predator density dependence, extinction, non-persistence in the mean, weak and strong persistence in the mean

Abstract

The non-autonomous stochastic density dependent predator-prey model with Holling-type II functional response disturbed by white noise, centered and non-centered Poisson noises is investigated. Corresponding system of stochastic differential equations has a unique, positive, global (no explosions in a finite time) solution. Sufficient conditions are obtained for extinction, non-persistence in the mean, weak and strong persistence in the mean of a predator and prey population densities in the considered stochastic predator-prey model.

Pages of the article in the issue: 30 - 36

Language of the article: English

References

IANNELLI, M., PUGLIESE, A. (2014) An Introduction to Mathematical Population Dynamics. Springer.

BORYSENKO, O. and BORYSENKO, OLG. (2022) A stochastic predator-prey model that depends on the population density of the predator. Bulletin of Taras Shevchenko National University of Kyiv, Series: Physics & Mathematics. no.4. pp.11-17.

BORYSENKO, OLG. and BORYSENKO,O. (2021) Long-time behavior of a non-autonomous stochastic predator-prey model with jumps Modern Stochastics: Theory and Applications. 8(1). p.17-39.

BORYSENKO, O. and BORYSENKO, OLG. (2022) Long-Time Behavior of Stochastic Models of Population Dynamics with Jumps. Stochastic Processes: Fundamentals and Emerging Applications. Ed. by Mikhail Moklyachuk. New York, NY: Nova Science Publishers. pp. 37-63.

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. 2(99), pp.63-70.

LIPSTER, R. (1980) A strong law of large numbers for local martingales. Stochastics. vol. 3. pp. 217-228.

LIU, M., WANGA, K. (2011) Persistence and extinction in stochastic non-autonomous logistic systems. Journal of Mathematical Analysis and Applications. 375, pp. 443-457.

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Published

2023-07-13

How to Cite

Borysenko, O. D., & Borysenko, O. V. (2023). Extinction and persistence in stochastic predator population density-dependent predator-prey model with jumps. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (1), 30–36. https://doi.org/10.17721/1812-5409.2023/1.4

Issue

Section

Algebra, Geometry and Probability Theory