Stochastic Delay Logistic Model under Regime Switching
This paper is concerned with a delay logistical model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall's inequality, and Young's inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate b...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/241702 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556010821124096 |
|---|---|
| author | Zheng Wu Hao Huang Lianglong Wang |
| author_facet | Zheng Wu Hao Huang Lianglong Wang |
| author_sort | Zheng Wu |
| collection | DOAJ |
| description | This paper is concerned with a delay logistical model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall's inequality, and Young's inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Also, the relationships between the stochastic permanence and extinction as well as asymptotic estimations of solutions are investigated by virtue of V-function technique, M-matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results. |
| format | Article |
| id | doaj-art-a4cd8549c7f14a0191af570f46ac0126 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a4cd8549c7f14a0191af570f46ac01262025-02-03T05:46:35ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/241702241702Stochastic Delay Logistic Model under Regime SwitchingZheng Wu0Hao Huang1Lianglong Wang2School of Mathematical Science, Anhui University, Hefei, Anhui 230039, ChinaSchool of Mathematical Science, Anhui University, Hefei, Anhui 230039, ChinaSchool of Mathematical Science, Anhui University, Hefei, Anhui 230039, ChinaThis paper is concerned with a delay logistical model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall's inequality, and Young's inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Also, the relationships between the stochastic permanence and extinction as well as asymptotic estimations of solutions are investigated by virtue of V-function technique, M-matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results.http://dx.doi.org/10.1155/2012/241702 |
| spellingShingle | Zheng Wu Hao Huang Lianglong Wang Stochastic Delay Logistic Model under Regime Switching Abstract and Applied Analysis |
| title | Stochastic Delay Logistic Model under Regime Switching |
| title_full | Stochastic Delay Logistic Model under Regime Switching |
| title_fullStr | Stochastic Delay Logistic Model under Regime Switching |
| title_full_unstemmed | Stochastic Delay Logistic Model under Regime Switching |
| title_short | Stochastic Delay Logistic Model under Regime Switching |
| title_sort | stochastic delay logistic model under regime switching |
| url | http://dx.doi.org/10.1155/2012/241702 |
| work_keys_str_mv | AT zhengwu stochasticdelaylogisticmodelunderregimeswitching AT haohuang stochasticdelaylogisticmodelunderregimeswitching AT lianglongwang stochasticdelaylogisticmodelunderregimeswitching |