Mathematical Biosciences and Engineering (MBE)

Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations

Pages: 1477 - 1498, Volume 14, Issue 5/6, October/December 2017      doi:10.3934/mbe.2017077

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Sanling Yuan - College of Science, Shanghai University for Science and Technology, Shanghai 200093, China (email)
Xuehui Ji - College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China (email)
Huaiping Zhu - Lamps and Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada (email)

Abstract: In this paper, we investigate the dynamics of a delayed logistic model with both impulsive and stochastic perturbations. The impulse is introduced at fixed moments and the stochastic perturbation is of white noise type which is assumed to be proportional to the population density. We start with the existence and uniqueness of the positive solution of the model, then establish sufficient conditions ensuring its global attractivity. By using the theory of integral Markov semigroups, we further derive sufficient conditions for the existence of the stationary distribution of the system. Finally, we perform the extinction analysis of the model. Numerical simulations illustrate the obtained theoretical results.

Keywords:  Delayed stochastic logistic model, impulsive perturbation, Itô's formula, stationary distribution, extinction.
Mathematics Subject Classification:  Primary: 65C20, 65C30; Secondary: 92D25.

Received: June 2016;      Accepted: September 2016;      Available Online: May 2017.