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Li, X., Alison, A., Jiang, D. and Mao, X. (2011) Sufficient and Necessary Conditions of Stochastic Permanence and Extinction for Stochastic Logistic Populations under Regime Switching. Journal of Mathematical Analysis and Applications, 376, 11-28.
https://doi.org/10.1016/j.jmaa.2010.10.053

has been cited by the following article:

• TITLE: Analysis of a Stochastic Ratio-Dependent Predator-Prey System with Markovian Switching and Lévy Jumps

  AUTHORS: Xuegui Zhang, Yuanfu Shao, Taolin Zhang

  KEYWORDS: Ratio-Dependent Predator-Prey System, Lévy, Stochastically Permanence, Ergodicity

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.11, November 27, 2020

  ABSTRACT: In this paper, the dynamics of a stochastic ratio-dependent predator-prey system with markovian switching and Lévy noise is studied. Firstly, we show the existence condition of global positive solution under the given positive initial value. Secondly, sufficient conditions for system extinction and persistence are obtained through some assumptions. Then, the sufficient conditions of stochastically persistence are obtained by combining stochastic analysis technique and M-matrix analysis. In addition, under appropriate conditions, we demonstrate the existence of a unique stationary distribution for a system without Lévy jumps. Finally, the empirical and Mlistein methods are used to verify the theoretical results through numerical simulation.