LIU Yingzi,LI Zhong,HE Mengxin.Dynamics analysis of a Leslie - Gower type predator - prey model with fear effect and prey refuge[J].Journal of Yanbian University,2022,(02):112-117.
具有恐惧效应和食饵避难所的Leslie - Gower捕食者-食饵模型的动力学分析
- Title:
- Dynamics analysis of a Leslie - Gower type predator - prey model with fear effect and prey refuge
- 文章编号:
- 1004-4353(2022)02-0112-06
- Keywords:
- predator - prey model; fear effect; refuge; population density; stability
- 分类号:
- O29
- 文献标志码:
- A
- 摘要:
- 对一类具有恐惧效应和食饵避难所的Leslie - Gower捕食者- 食饵模型的动力学行为进行了研究.首先,利用吹胀的方法研究了模型原点的稳定性,并通过计算模型平衡点的雅可比矩阵研究了模型的边界和正平衡点的稳定性.然后,利用Dulac判别法证明了模型的唯一正平衡点是全局渐近稳定的,并讨论了恐惧效应和食饵避难所对食饵和捕食者种群密度的影响.最后,利用数值模拟验证了所得结果的正确性.
- Abstract:
- The dynamic behaviors of a Leslie - Gower type predator - prey model with fear effect and prey refuge were investigated.Firstly, using blow - up method, the stability of the origin of the model was studied, and the stability of the boundary and positive equilibria of the model were analyzed by calculating the Jacobian matrix of the equilibria of the model.Secondly, the Dulac criterion is used to prove that the unique positive equilibrium point of the model is globally asymptotically stable, and the influence of fear effect and prey refuge on prey and predator population density were discussed.Finally, numerical simulations verified the accuracy of the results.
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相似文献/References:
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[2]王逸勤,施春玲.具有常数避难所和恐惧效应的HollingⅡ类功能性反应捕食食饵系统的定性分析[J].延边大学学报(自然科学版),2023,(02):116.
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[3]王檄豪,韦煜明.一类具有恐惧效应的时滞广义Holling Ⅲ型捕食者- 食饵模型的动力学分析[J].延边大学学报(自然科学版),2023,(04):288.
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备注/Memo
收稿日期: 2022-05-22
基金项目: 福建省自然科学基金(2021J01613; 2021J011032)
第一作者: 刘英姿(1997—),女,硕士研究生,研究方向为微分方程及其应用.
通信作者: 李忠(1980—),男,博士,副教授,研究方向为微分方程及其应用.