Persistence in mean and extinction on stochastic competitive Gilpin-Ayala systems with regime switching
Abstract We are interested in the persistence in mean and extinction for a stochastic competitive Gilpin-Ayala system with regime switching. Based on the stochastic LaSalle theorem and the space-decomposition method, we derive generalized sufficient criteria on persistence in mean and extinction. By...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-12-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1440-7 |
| _version_ | 1818303119281356800 |
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| author | Xiuli He Lei Liu Quanxin Zhu |
| author_facet | Xiuli He Lei Liu Quanxin Zhu |
| author_sort | Xiuli He |
| collection | DOAJ |
| description | Abstract We are interested in the persistence in mean and extinction for a stochastic competitive Gilpin-Ayala system with regime switching. Based on the stochastic LaSalle theorem and the space-decomposition method, we derive generalized sufficient criteria on persistence in mean and extinction. By constructing a novel Lyapunov function we establish sufficient criteria on partial persistence in mean and partial extinction for the system. Finally, we provide two examples to demonstrate the feasibility and validity of our proposed methods. |
| first_indexed | 2024-12-13T05:49:44Z |
| format | Article |
| id | doaj.art-7dd1082f72d3475c9c366f1ba927b557 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-13T05:49:44Z |
| publishDate | 2017-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-7dd1082f72d3475c9c366f1ba927b5572022-12-21T23:57:35ZengSpringerOpenAdvances in Difference Equations1687-18472017-12-012017112310.1186/s13662-017-1440-7Persistence in mean and extinction on stochastic competitive Gilpin-Ayala systems with regime switchingXiuli He0Lei Liu1Quanxin Zhu2College of Science, Hohai UniversityCollege of Science, Hohai UniversitySchool of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal UniversityAbstract We are interested in the persistence in mean and extinction for a stochastic competitive Gilpin-Ayala system with regime switching. Based on the stochastic LaSalle theorem and the space-decomposition method, we derive generalized sufficient criteria on persistence in mean and extinction. By constructing a novel Lyapunov function we establish sufficient criteria on partial persistence in mean and partial extinction for the system. Finally, we provide two examples to demonstrate the feasibility and validity of our proposed methods.http://link.springer.com/article/10.1186/s13662-017-1440-7Lotka-Volterra modelrandom environmentsBrownian motionsItô formulapersistence in meanextinction |
| spellingShingle | Xiuli He Lei Liu Quanxin Zhu Persistence in mean and extinction on stochastic competitive Gilpin-Ayala systems with regime switching Advances in Difference Equations Lotka-Volterra model random environments Brownian motions Itô formula persistence in mean extinction |
| title | Persistence in mean and extinction on stochastic competitive Gilpin-Ayala systems with regime switching |
| title_full | Persistence in mean and extinction on stochastic competitive Gilpin-Ayala systems with regime switching |
| title_fullStr | Persistence in mean and extinction on stochastic competitive Gilpin-Ayala systems with regime switching |
| title_full_unstemmed | Persistence in mean and extinction on stochastic competitive Gilpin-Ayala systems with regime switching |
| title_short | Persistence in mean and extinction on stochastic competitive Gilpin-Ayala systems with regime switching |
| title_sort | persistence in mean and extinction on stochastic competitive gilpin ayala systems with regime switching |
| topic | Lotka-Volterra model random environments Brownian motions Itô formula persistence in mean extinction |
| url | http://link.springer.com/article/10.1186/s13662-017-1440-7 |
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