Asymptotic Analysis of Impulsive Dispersal Predator-Prey Systems with Markov Switching on Finite-State Space
In this paper, we investigate the stochastic dynamics of two dispersal predator-prey systems perturbed by white noise, impulsive effect, and regime switching. For the system just interrupted by white noise, we first prove that the stochastic impulsive system has a nontrivial positive periodic soluti...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/8057153 |
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| _version_ | 1832548880168779776 |
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| author | Guodong Liu Zhengbo Chang Xinzhu Meng |
| author_facet | Guodong Liu Zhengbo Chang Xinzhu Meng |
| author_sort | Guodong Liu |
| collection | DOAJ |
| description | In this paper, we investigate the stochastic dynamics of two dispersal predator-prey systems perturbed by white noise, impulsive effect, and regime switching. For the system just interrupted by white noise, we first prove that the stochastic impulsive system has a nontrivial positive periodic solution. Then the sufficient conditions for persistence in mean and extinction of the system are obtained. For the system with Markov regime switching, we verify it is ergodic and has a stationary distribution. And conditions for extinction of the prey species are established. Finally, we provide a series of numerical simulations to illustrate the theoretical analysis. |
| format | Article |
| id | doaj-art-43127f22cb254301901d54c2e113705c |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-43127f22cb254301901d54c2e113705c2025-02-03T06:12:42ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/80571538057153Asymptotic Analysis of Impulsive Dispersal Predator-Prey Systems with Markov Switching on Finite-State SpaceGuodong Liu0Zhengbo Chang1Xinzhu Meng2College 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, ChinaIn this paper, we investigate the stochastic dynamics of two dispersal predator-prey systems perturbed by white noise, impulsive effect, and regime switching. For the system just interrupted by white noise, we first prove that the stochastic impulsive system has a nontrivial positive periodic solution. Then the sufficient conditions for persistence in mean and extinction of the system are obtained. For the system with Markov regime switching, we verify it is ergodic and has a stationary distribution. And conditions for extinction of the prey species are established. Finally, we provide a series of numerical simulations to illustrate the theoretical analysis.http://dx.doi.org/10.1155/2019/8057153 |
| spellingShingle | Guodong Liu Zhengbo Chang Xinzhu Meng Asymptotic Analysis of Impulsive Dispersal Predator-Prey Systems with Markov Switching on Finite-State Space Journal of Function Spaces |
| title | Asymptotic Analysis of Impulsive Dispersal Predator-Prey Systems with Markov Switching on Finite-State Space |
| title_full | Asymptotic Analysis of Impulsive Dispersal Predator-Prey Systems with Markov Switching on Finite-State Space |
| title_fullStr | Asymptotic Analysis of Impulsive Dispersal Predator-Prey Systems with Markov Switching on Finite-State Space |
| title_full_unstemmed | Asymptotic Analysis of Impulsive Dispersal Predator-Prey Systems with Markov Switching on Finite-State Space |
| title_short | Asymptotic Analysis of Impulsive Dispersal Predator-Prey Systems with Markov Switching on Finite-State Space |
| title_sort | asymptotic analysis of impulsive dispersal predator prey systems with markov switching on finite state space |
| url | http://dx.doi.org/10.1155/2019/8057153 |
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