Periodic solutions for a stochastic non-autonomous Holling–Tanner predator–prey system with impulses. (November 2016)

• Record Type: Journal Article
• Authors: Zuo, Wenjie; Jiang, Daqing
• Is Part Of: Nonlinear analysis. Volume 22(2016)
• Page Start: 191
• Page End: 201
• Publication Date: 2016-11
• Subjects: Holling–Tanner predator–prey system -- Stochastic perturbance -- Impulsive effect -- Periodic solution -- Global attraction; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2016.03.004
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: A stochastic non-autonomous Holling–Tanner predator–prey system with impulsive effect is investigated. First, we prove the existence and uniqueness of the global positive solution by constructing the equivalent system without impulse. Second, we give the sufficient condition for the existence of positive T -periodic solution by choosing a suitable Lyapunov function. Third, we prove the existence and global attraction of the boundary periodic solution by using the comparison theorem under a certain condition. Finally, numerical simulations illustrate our theoretical results, which show that the impulse or the white noises can result in the extinction of the predator in a certain condition. Highlights: A stochastic non-autonomous Holling–Tanner predator–prey system with impulsive effect is investigated. The existence and uniqueness of positive periodic solution is obtained by choosing a suitable Lyapunov function. The existence and global attraction of the boundary periodic solution is proved by using the comparison theorem. The result shows that, the impulses and white noises have much influence on the persistence and extinction of the predator.