| 摘要: |
| 具有反馈控制和Allee效应的偏利共生模型，其动力学行为比较复杂 .在反馈控制偏利共生模型的基础上，研究加法Allee效应对系统的动力学行为的影响，证明了系统正平衡点存在的条件足以保证系统的全局吸引性 .通过构造适当的Lyapunov函数，得到平衡点全局稳定的充分条件.研究表明：Allee效应不影响反馈控制偏利共生系统平衡点的稳定性，但会影响平衡点的位置. |
| 关键词: 偏利共生系统 反馈控制 Allee效应 全局稳定性 |
| DOI：10.3969/J.ISSN.1000-5137.2022.03.021 |
| 分类号:O175.14 |
| 基金项目:The Natural Science Foundation of Fujian Province（2019J01841，2021J011155）；The Natural Science Foundation of Fujian Eduction Department（JAT200690） |
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| Dynamic behavior of commensal symbiosis system with both feedback control and Allee effect |
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XU Lili, LIN Qifa, LEI Chaoquan
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College of Mathematics and Physics, Ningde Normal University, Ningde 352000, Fujian, China
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| Abstract: |
| The dynamic behavior of commensal symbiosis system with both feedback control and Allee effect is complex. In this paper，the influence of additive Allee effect on the dynamical behavior of the system has been studied based on the feedback control commensal symbiosis system. It is proved that the conditions for the existence of positive equilibrium point are sufficient to ensure the global attractive of the system. By constructing an appropriate Lyapunov function，the sufficient conditions for the global stability of the equilibrium point are obtained. The research shows that Allee effect does not affect the stability of the equilibrium point of the feedback control biased commensal symbiosis system，but affects the position of the equilibrium point. |
| Key words: commensal symbiosis system feedback control Allee effect global stability |
