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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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| 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 |
| id | doaj-art-53e46aebdfd74beeabde521ba57879ac |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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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