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Liu, H.Y., Luo, J.G. and Zhao, X.H. (2003) On Criteria for Global Stability of N-Dimensional Lotka-Volterra Systems. Annals of Differential Equations, 19, 343-351.

has been cited by the following article:

• 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.