Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps

In this paper, we explore an impulsive stochastic infected predator-prey system with Lévy jumps and delays. The main aim of this paper is to investigate the effects of time delays and impulse stochastic interference on dynamics of the predator-prey model. First, we prove some properties of the subsy...

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Main Authors: Guodong Liu, Xiaohong Wang, Xinzhu Meng, Shujing Gao
Format: Article
Language:English
Published: Wiley 2017-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2017/1950970
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author Guodong Liu
Xiaohong Wang
Xinzhu Meng
Shujing Gao
author_facet Guodong Liu
Xiaohong Wang
Xinzhu Meng
Shujing Gao
author_sort Guodong Liu
collection DOAJ
description In this paper, we explore an impulsive stochastic infected predator-prey system with Lévy jumps and delays. The main aim of this paper is to investigate the effects of time delays and impulse stochastic interference on dynamics of the predator-prey model. First, we prove some properties of the subsystem of the system. Second, in view of comparison theorem and limit superior theory, we obtain the sufficient conditions for the extinction of this system. Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.
format Article
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institution Kabale University
issn 1076-2787
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language English
publishDate 2017-01-01
publisher Wiley
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series Complexity
spelling doaj-art-53e46aebdfd74beeabde521ba57879ac2025-02-03T01:28:56ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/19509701950970Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with JumpsGuodong Liu0Xiaohong Wang1Xinzhu Meng2Shujing Gao3College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaKey Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou 341000, ChinaIn this paper, we explore an impulsive stochastic infected predator-prey system with Lévy jumps and delays. The main aim of this paper is to investigate the effects of time delays and impulse stochastic interference on dynamics of the predator-prey model. First, we prove some properties of the subsystem of the system. Second, in view of comparison theorem and limit superior theory, we obtain the sufficient conditions for the extinction of this system. Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.http://dx.doi.org/10.1155/2017/1950970
spellingShingle Guodong Liu
Xiaohong Wang
Xinzhu Meng
Shujing Gao
Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps
Complexity
title Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps
title_full Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps
title_fullStr Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps
title_full_unstemmed Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps
title_short Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps
title_sort extinction and persistence in mean of a novel delay impulsive stochastic infected predator prey system with jumps
url http://dx.doi.org/10.1155/2017/1950970
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