Asymptotic behavior of a Lotka–Volterra food chain stochastic model in the Chemostat. Issue 4 (4th July 2017)

• Record Type: Journal Article
• Authors: Sun, Mingjuan; Dong, Qinglai; Wu, Jing
• Is Part Of: Stochastic analysis and applications. Volume 35:Issue 4(2017)
• Page Start: 645
• Page End: 661
• Publication Date: 2017-07-04
• Subjects: Chemostat -- food chain -- Itô's formula -- stability -- stationary distribution; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2017.1299628
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: This article studies the asymptotic behavior of a stochastic Chemostat model with Lotka–Volterra food chain in which the dilution rate was influenced by white noise. The long-time behavior of the model is studied. Using Lyapunov function and Itô's formula, we show that there is a unique positive solution to the system. Moreover, the sufficient conditions for some population dynamical properties including the boundedness in mean and the stochastically asymptotic stability of the washout equilibrium were obtained. Furthermore, we show how the solutions spiral around the predator-free equilibrium and the positive equilibrium of deterministic system. Besides, the existence of the stationary distribution is proved for the considered model. Numerical simulations are introduced finally to support the obtained results.