Dynamic analysis of a reaction–diffusion impulsive hybrid system. (August 2019)

• Record Type: Journal Article
• Authors: Liu, He; Yu, Hengguo; Dai, Chuanjun; Wang, Qi; Li, Jianbing; Agarwal, Ravi P.; Zhao, Min
• Is Part Of: Nonlinear analysis. Volume 33(2019)
• Page Start: 353
• Page End: 370
• Publication Date: 2019-08
• Subjects: Crowley–Martin functional response -- Reaction–diffusion equation -- Permanence -- Periodic solution -- Impulsive effect; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2019.03.001
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: In this paper, a predator–prey system with Crowley–Martin functional response, which is described by a couple of reaction–diffusion equations with impulsive, is studied analytically and numerically. The aim of this research is to analyze how the impulsive effect influences dynamics of the system. Dynamics of the system, including the ultimate boundedness, permanence and extinction, are investigated firstly under impulsive effects. Significantly, it is found that there exists a unique positive periodic solution that is globally asymptotically stable when impulsive effects reach some critical state. Additionally, a series of numerical simulations are carried out to further study the dynamics of the system, which are consistent with the analytical results.