Global asymptotic behavior of a multi-species stochastic chemostat model with discrete delays
We consider a model of multi-species competition in the chemostat that includes demographic stochasticity and discrete delays. We prove that for any given initial data, there exists a unique global positive solution for the stochastic delayed system. By employing the method of stochastic Lyapunov fu...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2020
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| Online Access: | https://hdl.handle.net/10356/144320 |
| _version_ | 1811688747943591936 |
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| author | Wang, Liang Jiang, Daqing Wolkowicz, Gail S. K. |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Wang, Liang Jiang, Daqing Wolkowicz, Gail S. K. |
| author_sort | Wang, Liang |
| collection | NTU |
| description | We consider a model of multi-species competition in the chemostat that includes demographic stochasticity and discrete delays. We prove that for any given initial data, there exists a unique global positive solution for the stochastic delayed system. By employing the method of stochastic Lyapunov functionals, we determine the asymptotic behaviors of the stochastic solution and show that although the sample path fluctuate, it remains positive and the expected time average of the distance between the stochastic solution and the equilibrium of the associated deterministic delayed chemostat model is eventually small, i.e. we obtain an analogue of the competition exclusion principle when the noise intensities are relatively small. Numerical simulations are carried out to illustrate our theoretical results. |
| first_indexed | 2024-10-01T05:37:08Z |
| format | Journal Article |
| id | ntu-10356/144320 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:37:08Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1443202023-02-28T19:56:45Z Global asymptotic behavior of a multi-species stochastic chemostat model with discrete delays Wang, Liang Jiang, Daqing Wolkowicz, Gail S. K. School of Physical and Mathematical Sciences Science::Chemistry Chemostat Stochastic System We consider a model of multi-species competition in the chemostat that includes demographic stochasticity and discrete delays. We prove that for any given initial data, there exists a unique global positive solution for the stochastic delayed system. By employing the method of stochastic Lyapunov functionals, we determine the asymptotic behaviors of the stochastic solution and show that although the sample path fluctuate, it remains positive and the expected time average of the distance between the stochastic solution and the equilibrium of the associated deterministic delayed chemostat model is eventually small, i.e. we obtain an analogue of the competition exclusion principle when the noise intensities are relatively small. Numerical simulations are carried out to illustrate our theoretical results. Accepted version 2020-10-28T06:13:52Z 2020-10-28T06:13:52Z 2019 Journal Article Wang, L., Jiang, D., & Wolkowicz, G. S. K. (2020). Global asymptotic behavior of a multi-species stochastic chemostat model with discrete delays. Journal of Dynamics and Differential Equations, 32(2), 849-872. doi:10.1007/s10884-019-09741-6 1040-7294 https://hdl.handle.net/10356/144320 10.1007/s10884-019-09741-6 2 32 849 872 en Journal of Dynamics and Differential Equations © 2019 Springer Science+Business Media. This is a post-peer-review, pre-copyedit version of an article published in Journal of Dynamics and Differential Equations. The final authenticated version is available online at: http://dx.doi.org/0.1007/s10884-019-09741-6 application/pdf |
| spellingShingle | Science::Chemistry Chemostat Stochastic System Wang, Liang Jiang, Daqing Wolkowicz, Gail S. K. Global asymptotic behavior of a multi-species stochastic chemostat model with discrete delays |
| title | Global asymptotic behavior of a multi-species stochastic chemostat model with discrete delays |
| title_full | Global asymptotic behavior of a multi-species stochastic chemostat model with discrete delays |
| title_fullStr | Global asymptotic behavior of a multi-species stochastic chemostat model with discrete delays |
| title_full_unstemmed | Global asymptotic behavior of a multi-species stochastic chemostat model with discrete delays |
| title_short | Global asymptotic behavior of a multi-species stochastic chemostat model with discrete delays |
| title_sort | global asymptotic behavior of a multi species stochastic chemostat model with discrete delays |
| topic | Science::Chemistry Chemostat Stochastic System |
| url | https://hdl.handle.net/10356/144320 |
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