| 具有反馈控制和时滞的比率依赖随机Lotka-Volterra竞争-合作模型的动力学分析 |
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| 引用本文： | 蒙诚霖,刘萍,谢婷,韩秋珂.具有反馈控制和时滞的比率依赖随机Lotka-Volterra竞争-合作模型的动力学分析[J].云南大学学报(自然科学版),2023,45(2):276-283. |
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| 作者姓名： | 蒙诚霖 刘萍 谢婷 韩秋珂 |
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| 作者单位： | 云南大学 数学与统计学院，云南 昆明 650500 |
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| 基金项目： | 国家自然科学基金（11961078）； |
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| 摘 要： | 研究了一类新的具有反馈控制和时滞的比率依赖随机三种群Lotka-Volterra竞争-合作生物模型.首先，证明了模型存在唯一的全局正解.其次，通过构造适当的Lyapunov函数，证明了模型的解是随机最终有界的.最后，运用伊藤公式和微分不等式放缩，得到了种群灭绝的充分条件.
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| 关 键 词： | 随机Lotka-Volterra竞争-合作模型 反馈控制 全局正解 随机最终有界 |
| 收稿时间： | 2022-10-20 |
Dynamics analysis of a ratio-dependent stochastic Lotka-Volterra competition-cooperation model with feedback control and time delays |
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| MENG Cheng-lin,LIU Ping,XIE Ting,HAN Qiu-ke.Dynamics analysis of a ratio-dependent stochastic Lotka-Volterra competition-cooperation model with feedback control and time delays[J].Journal of Yunnan University(Natural Sciences),2023,45(2):276-283. |
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| Authors: | MENG Cheng-lin LIU Ping XIE Ting HAN Qiu-ke |
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| Institution: | School of Mathematics and Statistics, Yunnan University, Kunming 650500, Yunnan, China |
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| Abstract: | A new class of ratio-dependent stochastic three-group Lotka-Volterra competition cooperation model with feedback control and time delays is investigated in this paper. Firstly, we prove that system has a unique global positive solution. Further, the stochastic ultimate boundedness of the solution for system is investigated by constructing appropriate Lyapunov function. Finally, sufficient conditions for populations extinction are obtained by using It? formula and differential inequality scaling. |
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| Keywords: | stochastic Lotka-Volterra competitive-cooperative model feedback control global positive solution stochastically ultimate boundedness |
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