WANG Yiqin,SHI Chunling.Qualitative analysis of a predator-prey system with Holling type Ⅱ functional response incorporating fear effct and a constant prey refuge[J].Journal of Yanbian University,2023,(02):116-121+135.
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
- Title:
- Qualitative analysis of a predator-prey system with Holling type Ⅱ functional response incorporating fear effct and a constant prey refuge
- Keywords:
- predator-prey system; refuge; fear effect; limit cycle; global stability; equilibrium point
- 分类号:
- O175
- 文献标志码:
- A
- 摘要:
- 为了研究恐惧效应对具有避难所的功能性反应捕食食饵系统的影响,建立了一类具有常数避难所和恐惧效应的Ⅱ类功能性反应捕食食饵系统.首先,利用Lyapunov稳定性判别法研究了系统平衡点的局部稳定性,并利用Bendixson-Dulac定理得到了系统正解的全局稳定性;其次,利用Poincare-Bendixson定理获得了系统极限环的存在性;最后,对恐惧效应对系统稳定性的影响以及恐惧效应和避难所对种群密度的影响进行了分析,结果显示适当的恐惧水平和避难所有利于食饵和捕食者共存.
- Abstract:
- In order to study the effect of fear on the predator-prey system with functional incorporating refuge, a new predator-prey system with Holling type Ⅱ functional response incorporating fear effct and a constant prey refuge was established.Firstly, by using Lyapunov stability discriminance, the conditions of the instability and stability properties to the equilibrias were obtained, and the global stability of the positive solution of the system were given with Bendixson-Dulac theorem.Secondly, the existence to limit cycles for the system was found with Poincare-Bendixson theorem.Finally, the influence of fear effect on the stability of the system and the influence of fear effect and prey refuge on the pupulation density were analyzed, it showed that a certain level of fear and shelter were beneficial to the coexistence of prey and predator.
参考文献/References:
[1] CHEN L J,CHEN F D,CHEN L J.Qualitative analysis of a predator-prey model with Holling type Ⅱ functional response incorporating a constant prey refuge[J].Nonlinear Analysis:Real World Applications,2010,11:246-252.
[2] WANG X,ZANETTE L,ZOU X.Modelling the fear effect in predator-prey interactions[J].Journal of Mathematical Biology,2016,73(5):1179-1204.
[3] 刘英姿,李忠,何梦昕.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[J].延边大学学报(自然科学版),2022,2(6):112-117.
[4] WANG X Q,TAN Y P,CAI Y L,et al.Impact of the fear effect on the stability and bifurcation of a Leslie-Gower predator-prey model[J].International Journal of Bifurcation and Chaos,2020,30(14):205-210.
[5] ZHANG H S,CAI Y L,FU S M,et al.Impact of the fear effect in a prey-predator model incorporating a prey refuge[J].App Math Comput,2019,356:328-337.
[6] UPADHYAY R,MISHRA S.Popualtion dynamic consequences of fearful prey in a spatiotemporal predator-prey system[J].Math Biosci Eng,2018,16(1):338-372.
[7] WANG J,CAI Y L,FU S M,et al.The effect of the fear factor on the dynamics of a predator-prey model incorpating the prey refuge[J].Chaos,2019,29(8):83-109.
[8] LI Y,HE M,LI Z.Dynamics of a ratio-dependent Leslie-Gower predator-prey model with Allect effect and fear effect[J].Mathematics and Computers in Simulation,2022,32(6):2250082.
[9] 马知恩,周义仓,李承治.常微分方程定性与稳定性方法[M].北京:科学出版社,2015:182-183.
[10] MEISS J D.Differential dynamical systems[M].Philadelphia:Society for Industrial and Applied Mathematics,2007.
相似文献/References:
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[2]刘英姿,李忠,何梦昕.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[J].延边大学学报(自然科学版),2022,(02):112.
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备注/Memo
收稿日期: 2023 03 27
基金项目: 福建省自然科学基金(2019J01783);福建省教育厅中青年教师教育科研项目(JAT191174);福建省高校新世纪优秀人才支持计划(ZJ1891)
第一作者: 王逸勤(1978—),女,硕士,副教授,研究方向为微分方程及其应用.
通信作者: 施春玲(1979—),女,硕士,副教授,研究方向为微分方程及其应用.