Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps
This article concerns the study of stochastic Gilpin-Ayala mutualism models with white noise and Poisson jumps. Firstly, an explicit solution for one-dimensional Gilpin-Ayala mutualism model with jumps is obtained and the asymptotic pathwise behavior is analyzed. Then, sufficient conditions for...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2013-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/162/abstr.html |
| _version_ | 1818755424255475712 |
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| author | Xinhong Zhang Ke Wang |
| author_facet | Xinhong Zhang Ke Wang |
| author_sort | Xinhong Zhang |
| collection | DOAJ |
| description | This article concerns the study of stochastic Gilpin-Ayala mutualism models with white noise and Poisson jumps. Firstly, an explicit solution for one-dimensional Gilpin-Ayala mutualism model with jumps is obtained and the asymptotic pathwise behavior is analyzed. Then, sufficient conditions for the existence of global positive solutions, stochastically ultimate boundedness and stochastic permanence are established for the n-dimensional model. Asymptotic pathwise behavior of n-dimensional Gilpin-Ayala mutualism model with jumps is also discussed. Finally numerical examples are introduced to illustrate the results developed. |
| first_indexed | 2024-12-18T05:38:55Z |
| format | Article |
| id | doaj.art-7076a428da214868929bee457ee36e2a |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-18T05:38:55Z |
| publishDate | 2013-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-7076a428da214868929bee457ee36e2a2022-12-21T21:19:14ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-07-012013162,117Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumpsXinhong ZhangKe WangThis article concerns the study of stochastic Gilpin-Ayala mutualism models with white noise and Poisson jumps. Firstly, an explicit solution for one-dimensional Gilpin-Ayala mutualism model with jumps is obtained and the asymptotic pathwise behavior is analyzed. Then, sufficient conditions for the existence of global positive solutions, stochastically ultimate boundedness and stochastic permanence are established for the n-dimensional model. Asymptotic pathwise behavior of n-dimensional Gilpin-Ayala mutualism model with jumps is also discussed. Finally numerical examples are introduced to illustrate the results developed.http://ejde.math.txstate.edu/Volumes/2013/162/abstr.htmlGilpin-Ayala mutualism modeljumpsmoment boundednessasymptotic behaviorstochastic permanence |
| spellingShingle | Xinhong Zhang Ke Wang Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps Electronic Journal of Differential Equations Gilpin-Ayala mutualism model jumps moment boundedness asymptotic behavior stochastic permanence |
| title | Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps |
| title_full | Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps |
| title_fullStr | Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps |
| title_full_unstemmed | Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps |
| title_short | Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps |
| title_sort | asymptotic behavior of stochastic gilpin ayala mutualism model with jumps |
| topic | Gilpin-Ayala mutualism model jumps moment boundedness asymptotic behavior stochastic permanence |
| url | http://ejde.math.txstate.edu/Volumes/2013/162/abstr.html |
| work_keys_str_mv | AT xinhongzhang asymptoticbehaviorofstochasticgilpinayalamutualismmodelwithjumps AT kewang asymptoticbehaviorofstochasticgilpinayalamutualismmodelwithjumps |