1. Stationary distribution of a regime-switching predator–prey model with anti-predator behaviour and higher-order perturbations.
- Author
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Liu, Qun, Jiang, Daqing, Hayat, Tasawar, and Alsaedi, Ahmed
- Subjects
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DISTRIBUTION (Probability theory) , *LOTKA-Volterra equations , *PERTURBATION theory , *ERGODIC theory , *LYAPUNOV functions , *STOCHASTIC processes - Abstract
Abstract In this paper, we study a regime-switching predator–prey model with anti-predator behaviour and higher-order perturbations. We obtain the ergodic property by constructing a suitable stochastic Lyapunov function with regime-switching, which provides us a biological perspective of cycling phenomena of a population system, and can better describe the stochastic persistence of a population system in practice. We find that these restrictive assumptions on the functional response are relative weak and valid for many types of response functions. Highlights • A regime-switching predator–prey model with anti-predator behaviour is studied. • We obtain the ergodic property by constructing a suitable stochastic Lyapunov function. • The existence of a stationary distribution implies stochastic weak stability. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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