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Peng, S.G. and Zhu, X.H. (2006) Necessary and Sufficient Condition for Comparison Theorem of 1-Dimensional Stochastic Differential Equations. Stochastic Processes and Their Applications, 116, 370-380.
https://doi.org/10.1016/j.spa.2005.08.004

has been cited by the following article:

• TITLE: Global Dynamics of a Stochastic Two-Prey One-Predator Model with S-Type Distributed Delays and Lévy Noises

  AUTHORS: Taolin Zhang, Yuanfu Shao, Xiaowan She

  KEYWORDS: Distributed Delays, Lévy Noises, Global Attractivity, Stability in Distribution

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.9, September 28, 2020

  ABSTRACT: In this paper, a stochastic two-prey one-predator model with S-type distributed time delays and Lévy noises is considered. Using the comparison theorem and Ito’s formula, sufficient conditions of persistence in the mean and extinct for each population are established. Then, conditions of global attractivity and stability in distribution by Barbalat’s conclusion are also obtained. Furthermore, Euler numerical simulation method is given to demonstrate our conclusions.