Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations
In this paper, we investigate the dynamics of a delayed logistic model with both impulsive and stochastic perturbations. The impulse is introduced at fixed moments and the stochastic perturbation is of white noise type which is assumed to be proportional to the population density. We start with the...
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017077 |
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| author | Sanling Yuan Xuehui Ji Huaiping Zhu |
| author_facet | Sanling Yuan Xuehui Ji Huaiping Zhu |
| author_sort | Sanling Yuan |
| collection | DOAJ |
| description | In this paper, we investigate the dynamics of a delayed logistic model with both impulsive and stochastic perturbations. The impulse is introduced at fixed moments and the stochastic perturbation is of white noise type which is assumed to be proportional to the population density. We start with the existence and uniqueness of the positive solution of the model, then establish sufficient conditions ensuring its global attractivity. By using the theory of integral Markov semigroups, we further derive sufficient conditions for the existence of the stationary distribution of the system. Finally, we perform the extinction analysis of the model. Numerical simulations illustrate the obtained theoretical results. |
| format | Article |
| id | doaj-art-4d2365733b28466b808d63468aabdfa7 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-4d2365733b28466b808d63468aabdfa72025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61477149810.3934/mbe.2017077Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbationsSanling Yuan0Xuehui Ji1Huaiping Zhu2College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaLamps and Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, CanadaIn this paper, we investigate the dynamics of a delayed logistic model with both impulsive and stochastic perturbations. The impulse is introduced at fixed moments and the stochastic perturbation is of white noise type which is assumed to be proportional to the population density. We start with the existence and uniqueness of the positive solution of the model, then establish sufficient conditions ensuring its global attractivity. By using the theory of integral Markov semigroups, we further derive sufficient conditions for the existence of the stationary distribution of the system. Finally, we perform the extinction analysis of the model. Numerical simulations illustrate the obtained theoretical results.https://www.aimspress.com/article/doi/10.3934/mbe.2017077delayed stochastic logistic modelimpulsive perturbationitô's formulastationary distributionextinction |
| spellingShingle | Sanling Yuan Xuehui Ji Huaiping Zhu Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations Mathematical Biosciences and Engineering delayed stochastic logistic model impulsive perturbation itô's formula stationary distribution extinction |
| title | Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations |
| title_full | Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations |
| title_fullStr | Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations |
| title_full_unstemmed | Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations |
| title_short | Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations |
| title_sort | asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations |
| topic | delayed stochastic logistic model impulsive perturbation itô's formula stationary distribution extinction |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017077 |
| work_keys_str_mv | AT sanlingyuan asymptoticbehaviorofadelayedstochasticlogisticmodelwithimpulsiveperturbations AT xuehuiji asymptoticbehaviorofadelayedstochasticlogisticmodelwithimpulsiveperturbations AT huaipingzhu asymptoticbehaviorofadelayedstochasticlogisticmodelwithimpulsiveperturbations |