Dynamics of a ratio-dependent three-species food-chain system in a random environment

Article type: Research Article

Authors: Shi, Peilin^a | Dong, Lingzhen^{b; *}

Affiliations: [a] College of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China | [b] College of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We consider a system of stochastic differential equations, which is established by introducing white noises into a periodic and ratio-dependent food-chain system of three-species. We investigate the asymptotic behaviors for such a system, and obtain the sufficient conditions for its extinction and persistence with the help of Itô’s formula. We discuss the existence of a nontrivial positive periodic solution based on Has’minskii theory of periodic solution. Further, we study a ratio-dependent food-chain system of three-species including not only white noise but also telephone noise. For such a model, we give the sufficient conditions to guarantee the existence of a unique ergodic stationary distribution.

Keywords: Ratio-dependent food-chain systems, Itô’s formula, extinction and persistence, stochastic periodic solution, stationary distribution

DOI: 10.3233/ASY-241927

Journal: Asymptotic Analysis, vol. Pre-press, no. Pre-press, pp. 1-20, 2024