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Periodic Solution for a Stochastic Non-autonomous Predator-Prey Model with Holling II Functional Response

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Abstract

A biological population may be subjected to stochastic disturbance and exhibit periodicity. In this paper, a stochastic non-autonomous predator-prey system with Holling II functional response is proposed, and the existence of a unique positive solution is derived. We give sufficient conditions for extinction and strong persistence in the mean by analyzing a corresponding one-dimensional stochastic system. Also we establish the existence of positive periodic solutions for this stochastic non-autonomous predator-prey system. Finally, we use numerical simulations to illustrate our results and we present some conclusions and future directions. The results of this paper provide methods for other stochastic population models, which we hope to analyze in the future.

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Author information

Authors and Affiliations

  1. College of Mathematics and Statistics, Hainan Normal University, Hainan, 571158, P.R. China

    Li Zu

  2. School of Science, China University of Petroleum (East China), Qingdao, 266580, P.R. China

    Daqing Jiang

  3. Nonlinear Analysis and Applied Mathematics (NAAM)—Research Group, King Abdulaziz University, Jeddah, Saudi Arabia

    Daqing Jiang

  4. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

Authors
  1. Li Zu
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  2. Daqing Jiang
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  3. Donal O’Regan
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Corresponding author

Correspondence to Daqing Jiang.

Additional information

The work was supported by Program for NSFC of China (No.: 11371085), the Fundamental Research Funds for the Central Universities (No.: 15CX08011A), the Foundation of Hainan province colleges and universities scientific research projects (No.: Hnky2017ZD-14) and Hainan Province Natural Science Foundation of China (No.: 2018CXTD338).

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Zu, L., Jiang, D. & O’Regan, D. Periodic Solution for a Stochastic Non-autonomous Predator-Prey Model with Holling II Functional Response. Acta Appl Math 161, 89–105 (2019). https://doi.org/10.1007/s10440-018-0205-y

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  • DOI: https://doi.org/10.1007/s10440-018-0205-y

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