Dynamics analysis and numerical simulations of a stochastic non-autonomous predator–prey system with impulsive effects. (November 2017)

• Record Type: Journal Article
• Authors: Zhang, Shengqiang; Meng, Xinzhu; Feng, Tao; Zhang, Tonghua
• Is Part Of: Nonlinear analysis. Volume 26(2017)
• Page Start: 19
• Page End: 37
• Publication Date: 2017-11
• Subjects: Non-autonomous predator–prey model -- Impulsive effect -- Stochastic persistence -- Extinction -- Stochastic perturbation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2017.04.003
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: In this paper, we propose a stochastic non-autonomous Lotka–Volterra predator–prey model with impulsive effects and investigate its stochastic dynamics. We first prove that the subsystem of the system has a unique periodic solution which is globally attractive. Furthermore, we obtain the threshold value in the mean which governs the stochastic persistence and the extinction of the prey–predator system. Our results show that the stochastic noises and impulsive perturbations have crucial effects on the persistence and extinction of each species. Finally, we use the different stochastic noises and impulsive effects parameters to provide a series of numerical simulations to illustrate the analytical results. Highlights: An impulsive stochastic non-autonomous Lotka–Volterra predator–prey model is proposed and investigated. The existence and global attraction of the positive periodic solution of the subsystem are proved. The thresholds for stochastic persistence and extinction of the system are obtained. The developed numerical method for simulating the global stochastic dynamics of the model.