TITLE:
The Stochastic Asymptotic Stability Analysis in Two Species Lotka-Volterra Model
AUTHORS:
Yuqin Li, Yuehua He
KEYWORDS:
Asymptotic Stability, Stochastic Lotka-Volterra Model, Lyapunov Method
JOURNAL NAME:
Applied Mathematics,
Vol.14 No.7,
July
27,
2023
ABSTRACT: The asymptotic stability of two species stochastic Lotka-Volterra model is explored in this paper. Firstly, the Lotka-Volterra model with random parameter is built and reduced into the equivalent deterministic system by orthogonal polynomial approximation. Then, the linear stability theory and Routh-Hurwitz criterion for nonlinear deterministic systems are applied to the equivalent one. At last, at the aid of Lyapunov second method, we obtain that as the random intensity or statistical parameter of random variable is changed, the stability about stochastic Lotka-Volterra model is different from the deterministic system.