Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction
Considering periodic environmental changes and random disturbance, we explore the dynamical behaviors of a stochastic competitive system with impulsive and periodic parameters in this paper. Firstly, by use of extreme-value theory of quadratic function and constructing suitable functional, we study...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/1053401 |
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| author | Weili Kong Yuanfu Shao |
| author_facet | Weili Kong Yuanfu Shao |
| author_sort | Weili Kong |
| collection | DOAJ |
| description | Considering periodic environmental changes and random disturbance, we explore the dynamical behaviors of a stochastic competitive system with impulsive and periodic parameters in this paper. Firstly, by use of extreme-value theory of quadratic function and constructing suitable functional, we study the existence of periodic Markovian process. Secondly, by comparison theory of the stochastic differential equation, we study the extinction and permanence in the mean of all species. Thirdly, applying an important lemma, we investigate the stochastic persistence of this system. Finally, some numerical simulations are given to illustrate the main results. |
| format | Article |
| id | doaj-art-74a10a3d6400486993cc0a35df462798 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-74a10a3d6400486993cc0a35df4627982025-02-03T06:46:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/10534011053401Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-InteractionWeili Kong0Yuanfu Shao1College of Teacher Education, Qujing Normal University, Qujing, Yunnan 655011, ChinaCollege of Science, Guilin University of Technology, Guilin, Guangxi 541004, ChinaConsidering periodic environmental changes and random disturbance, we explore the dynamical behaviors of a stochastic competitive system with impulsive and periodic parameters in this paper. Firstly, by use of extreme-value theory of quadratic function and constructing suitable functional, we study the existence of periodic Markovian process. Secondly, by comparison theory of the stochastic differential equation, we study the extinction and permanence in the mean of all species. Thirdly, applying an important lemma, we investigate the stochastic persistence of this system. Finally, some numerical simulations are given to illustrate the main results.http://dx.doi.org/10.1155/2020/1053401 |
| spellingShingle | Weili Kong Yuanfu Shao Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction Discrete Dynamics in Nature and Society |
| title | Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction |
| title_full | Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction |
| title_fullStr | Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction |
| title_full_unstemmed | Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction |
| title_short | Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction |
| title_sort | stochastic periodic solution and persistence of a nonautonomous impulsive system with nonlinear self interaction |
| url | http://dx.doi.org/10.1155/2020/1053401 |
| work_keys_str_mv | AT weilikong stochasticperiodicsolutionandpersistenceofanonautonomousimpulsivesystemwithnonlinearselfinteraction AT yuanfushao stochasticperiodicsolutionandpersistenceofanonautonomousimpulsivesystemwithnonlinearselfinteraction |