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Volume 4, Issue 4
Asymptotic Behavior of a Stochastic Predator-Prey Model with Beddington-DeAngelis Functional Response and Lévy Jumps

Yaru Guo & Shulin Sun

DOI: 10.12150/jnma.2022.764

J. Nonl. Mod. Anal., 4 (2022), pp. 764-782.

Published online: 2023-08

[An open-access article; the PDF is free to any online user.]

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  • Abstract

A stochastic two-prey-one-predator model with Beddington-DeAngelis functional response and Lévy jumps is proposed and investigated in this paper. First of all, we prove the existence and uniqueness of the global positive solution, and stochastic ultimate boundedness of the solution. Next, under a simple assumption, by using Itô formula and other important inequalities, some sufficient conditions are established to ensure the extinction and persistence in the mean of the system. The results show that neither strong white noise nor Lévy noise is conducive to the persistence of the population. Finally, the theoretical results are verified by numerical simulations.

  • Keywords

Stochastic predator-prey model, Beddington-DeAngelis functional response, Lévy jump, Extinction, Persistence.

  • AMS Subject Headings

34K50, 60H10, 93E03

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-764, author = {Guo , Yaru and Sun , Shulin}, title = {Asymptotic Behavior of a Stochastic Predator-Prey Model with Beddington-DeAngelis Functional Response and Lévy Jumps}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {4}, number = {4}, pages = {764--782}, abstract = {

A stochastic two-prey-one-predator model with Beddington-DeAngelis functional response and Lévy jumps is proposed and investigated in this paper. First of all, we prove the existence and uniqueness of the global positive solution, and stochastic ultimate boundedness of the solution. Next, under a simple assumption, by using Itô formula and other important inequalities, some sufficient conditions are established to ensure the extinction and persistence in the mean of the system. The results show that neither strong white noise nor Lévy noise is conducive to the persistence of the population. Finally, the theoretical results are verified by numerical simulations.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.764}, url = {http://global-sci.org/intro/article_detail/jnma/21911.html} }
TY - JOUR T1 - Asymptotic Behavior of a Stochastic Predator-Prey Model with Beddington-DeAngelis Functional Response and Lévy Jumps AU - Guo , Yaru AU - Sun , Shulin JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 764 EP - 782 PY - 2023 DA - 2023/08 SN - 4 DO - http://doi.org/10.12150/jnma.2022.764 UR - https://global-sci.org/intro/article_detail/jnma/21911.html KW - Stochastic predator-prey model, Beddington-DeAngelis functional response, Lévy jump, Extinction, Persistence. AB -

A stochastic two-prey-one-predator model with Beddington-DeAngelis functional response and Lévy jumps is proposed and investigated in this paper. First of all, we prove the existence and uniqueness of the global positive solution, and stochastic ultimate boundedness of the solution. Next, under a simple assumption, by using Itô formula and other important inequalities, some sufficient conditions are established to ensure the extinction and persistence in the mean of the system. The results show that neither strong white noise nor Lévy noise is conducive to the persistence of the population. Finally, the theoretical results are verified by numerical simulations.

Yaru Guo & Shulin Sun. (2023). Asymptotic Behavior of a Stochastic Predator-Prey Model with Beddington-DeAngelis Functional Response and Lévy Jumps. Journal of Nonlinear Modeling and Analysis. 4 (4). 764-782. doi:10.12150/jnma.2022.764
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