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Periodic Solution and Stationary Distribution of Stochastic Predator–Prey Models with Higher-Order Perturbation

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Abstract

In this paper, two stochastic predator–prey models with general functional response and higher-order perturbation are proposed and investigated. For the nonautonomous periodic case of the system, by using Khasminskii’s theory of periodic solution, we show that the system admits a nontrivial positive T-periodic solution. For the system disturbed by both white and telegraph noises, sufficient conditions for positive recurrence and the existence of an ergodic stationary distribution to the solutions are established. The existence of stationary distribution implies stochastic weak stability to some extent.

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Acknowledgements

This work was supported by NSFC of China Grant No. 11371085, the Fundamental Research Funds for the Central Universities (No. 15CX08011A), 2016GXNSFBA380006 and KY2016YB370.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun, 130024, Jilin Province, People’s Republic of China

    Qun Liu & Daqing Jiang

  2. School of Mathematics and Statistics, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, Guangxi, People’s Republic of China

    Qun Liu

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

    Daqing Jiang

  4. College of Science, China University of Petroleum, Qingdao, 266580, Shandong Province, People’s Republic of China

    Daqing Jiang

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  1. Qun Liu
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  2. Daqing Jiang
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Correspondence to Daqing Jiang.

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Communicated by Oliver Junge.

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Liu, Q., Jiang, D. Periodic Solution and Stationary Distribution of Stochastic Predator–Prey Models with Higher-Order Perturbation. J Nonlinear Sci 28, 423–442 (2018). https://doi.org/10.1007/s00332-017-9413-2

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  • DOI: https://doi.org/10.1007/s00332-017-9413-2

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