Stationary distribution and periodic solutions for stochastic Holling–Leslie predator–prey systems

Daqing Jiang, Wenjie Zuo, Tasawar Hayat and Ahmed Alsaedi

Physica A: Statistical Mechanics and its Applications, 2016, vol. 460, issue C, 16-28

Abstract: The stochastic autonomous and periodic predator–prey systems with Holling and Leslie type functional response are investigated. For the autonomous system, we prove that there exists a unique stationary distribution, which is ergodic by constructing a suitable Lyapunov function under relatively small white noise. The result shows that, stationary distribution doesn’t rely on the existence and the stability of the positive equilibrium in the undisturbed system. Furthermore, for the corresponding non-autonomous system, we show that there exists a positive periodic Markov process under relatively weaker condition. Finally, numerical simulations illustrate our theoretical results.

Keywords: Stochastic predator–prey system; Holling and Leslie type; Stationary distribution; Ergodicity; Periodic solution (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:460:y:2016:i:c:p:16-28

DOI: 10.1016/j.physa.2016.04.037

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