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Liu, Q. and Jiang, D. (2019) Stationary Distribution and Extinction of a Stochastic One-Prey Two-Predator Model with Holling Type II Functional Response. Stochastic Analysis and Applications, 37, 321-345.
https://doi.org/10.1080/07362994.2019.1566005

has been cited by the following article:

• TITLE: On the Dynamics of a Stochastic Ratio-Dependent Predator-Prey System with Infection for the Prey

  AUTHORS: Jiying Ma, Haimiao Ren

  KEYWORDS: Stochastic Predator-Prey Model, Ratio-Dependent, Stationary Distribution, Extinction

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.11 No.4, April 21, 2021

  ABSTRACT: In this paper, we investigate the dynamics of a stochastic predator-prey model with ratio-dependent functional response and disease in the prey. Firstly, we prove the existence and uniqueness of the positive solution for the stochastic model by using conventional methods. Then we obtain the threshold for the infected prey population, that is, the disease will tend to extinction if > 1. Finally, the sufficient condition on the existence of a unique ergodic stationary distribution is obtained, which indicates that all the populations are permanent in the time mean sense. Numerical simulations are conducted to verify our analysis results.