食饵具有扩散和恐惧效应的捕食–食饵模型的稳定性分析
Stability Analysis of Predator-Prey Model with Dispersal and Fear Effect
DOI: 10.12677/AAM.2021.1011380, PDF,    科研立项经费支持
作者: 刘婷婷, 陈丽娟, 朱紫睿：福州大学数学与统计学院，福建 福州
关键词: 斑块扩散；恐惧效应；捕食–食饵系统；Patch Dispersal； Fear Effect； Predator-Prey System
摘要: 本文提出了一个食饵具有恐惧效应和扩散的捕食–食饵模型，通过定性分析，得到系统详尽的稳定性性态。我们还研究了恐惧效应对系统动力学行为的影响，同时还发现扩散对捕食者和食饵的持久性也有很大的影响。数值模拟进一步验证理论分析的正确性。
Abstract: In this paper, we propose a predator-prey model with fear effect and diffusion. By making full use of qualitative analysis, we obtain the detailed dynamic behavior of the system. We also study the influence of fear effect on the system and find that diffusion has a large effect on the persistence of predator and prey. Numerical simulation further demonstrates the feasibility of our theoretical conclusion.
文章引用：刘婷婷, 陈丽娟, 朱紫睿. 食饵具有扩散和恐惧效应的捕食–食饵模型的稳定性分析[J]. 应用数学进展, 2021, 10(11): 3601-3612. https://doi.org/10.12677/AAM.2021.1011380

参考文献

[1] Skellem, J.D. (1951) Dispersal in Theoretical Population. Biometrika, 38, 196-216. [Google Scholar] [CrossRef] [PubMed]
[2] Levin, S.A. (1974) Dispersal and Population Interactions. The American Naturalist, 108, 207-228. [Google Scholar] [CrossRef] 
[3] Freedman, H.I. and Waltman, D. (1977) Mathematical Models of Population Interactions with Dispersal: Stability of Two Habitats with and without a Predator. SIAM Journal on Applied Mathematics, 32, 631-648. [Google Scholar] [CrossRef] 
[4] Holt, R.D. (1985) Population Dynamics in Two-Patch Environments: Some Anomalous Consequences of an Optimal Habitat Distribution. Theoretical Population Biology, 28, 181-208. [Google Scholar] [CrossRef] 
[5] Lu, Z. and Takeuchi, Y. (1993) Global Asymptotic Behavior in Single-Species Discrete Diffusion Systems. Journal of Mathematical Biology, 32, 67-77. [Google Scholar] [CrossRef] 
[6] Chen, F.D., Chen, L.J. and Xie, X.D. (2009) On a Leslie-Gower Predator-Prey Model Incorporating a Prey Refuge. Nonlinear Analysis: Real World Applications, 10, 2904-2908. [Google Scholar] [CrossRef] 
[7] Wu, H., Wang, Y.S., Li, Y. and De Angelis, D.L. (2020) Dispersal Asymmetry in a Two-Patch System with Source-Sink Populations. Theoretical Population Biology, 131, 54-65. [Google Scholar] [CrossRef] [PubMed]
[8] Huang, R., Wang, Y.S. and Wu, H. (2020) Population Abundance in Predator-Prey Systems with Predators Dispersal between Two Patches. Theoretical Population Biology, 135, 1-8. [Google Scholar] [CrossRef] [PubMed]
[9] Liu, Z.G. (2018) The Effect of Prey Refuge in a Patchy Leslie-Gower Predation System. Acta Ecological Sinica, 38, 2958-2964. [Google Scholar] [CrossRef] 
[10] Wang, X.Y., Zanette, L.N. and Zou, X.F. (2016) Modelling the Fear Effect in Predator-Prey Interactions. Journal of Mathematical Biology, 73, 1179-1204. [Google Scholar] [CrossRef] [PubMed]
[11] Pal, S., .Pal, N. and Samanta, S. (2019) Effect of Hunting Cooperation and Fear in a Predator-Prey Model. Ecological Complexity, 39, 1-18. [Google Scholar] [CrossRef] 
[12] Zhang, H.S., Cai, Y.L., Fu, S.M. and Wang, W.M. (2019) Impact of the Fear Effect in a Prey-Predator Model Incorporating a Prey Refuge. Applied Mathematics and Computation, 356, 328-337. [Google Scholar] [CrossRef] 
[13] Das, M. and Samanta, G.P. (2021) A Prey-Predator Fractional Order Model with Fear Effect and Group Defense. International Journal of Dynamics and Control, 9, 334-349. [Google Scholar] [CrossRef] 
[14] Pal, S., Majhi, S., Mandal, S. and Pal, N. (2019) Role of Fear in a Predator-Prey Model with Beddington-DeAngelis Functional Response. Zeitschrift für Naturforschung, 74, 581-595. [Google Scholar] [CrossRef] 
[15] Kundu, K., Pal, S. and Samanta, S. (2019) Impact of Fear Effect in a Discrete-Time Predator-Prey System. Bulletion Calcutta Mathmatical Society, 110, 245-264.
[16] Pandy, P., Pal, N., Samanta, S. and Chattopadhyay, J. (2019) A Three Species Food Chain Model with Fear Induced Trophic Cascade. International Journal of Applied and Computational Mathematics, 5, Article No. 100. [Google Scholar] [CrossRef] 
[17] Wang, X.Y. and Zou, X.F. (2017) Modeling the Fear Effect in Predator-Prey Interactions with Adaptive Avoidance of Predators. Bulletin of Mathematical Biology, 79, 1325-1359. [Google Scholar] [CrossRef] [PubMed]
[18] 张芷芬, 丁同仁, 黄文灶, 董镇喜. 微分方程定性理论[M]. 北京: 科学出版社, 2014.
[19] 廖晓昕. 稳定性的理论、方法和应用[M]. 第2版. 武汉: 华中科技大学出版社, 2010.
[20] 陈兰荪. 数学生态学模型与研究方法[M]. 第2版. 北京: 科学出版社, 2017.

为你推荐