一类具有收获和恐惧效应的捕食生态模型动力学问题研究
Dynamical Analysis of a Predator-Prey Ecological Model with Harvesting and Fear Effect
摘要: 本文提出了一类具有线性收获和恐惧效应的Leslie-Gower捕食生态模型，推导出模型所有可能平衡点存在与稳定的临界条件，给出模型发生跨临界分岔、鞍结分岔、Hopf分岔的阈值条件，模拟出模型特定分岔动力学性态的演化进程，从分岔动力学的角度揭示种群生长共存模式及其内在驱动机制。希望这些结果有利于拓宽捕食生态模型复杂动力学问题研究框架。
Abstract: This paper proposed a Leslie-Gower predator-prey ecological model with linear harvesting and fear effect. The critical conditions for the existence and stability of all possible equilibrium points are derived. The threshold conditions for the occurrence of transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation are explored. The evolutionary processes of specific bifurcation dynamical behaviors are simulated. The population growth coexistence modes and their underlying driving mechanisms could be revealed from the perspective of bifurcation dynamics. In a word, it is my hope that these results will help broaden the research framework for complex dynamic problems of predator-prey ecological models.
文章引用：金成磊, 方靖哲, 曹中阳, 于恒国. 一类具有收获和恐惧效应的捕食生态模型动力学问题研究[J]. 应用数学进展, 2025, 14(8): 276-301. https://doi.org/10.12677/aam.2025.148389

参考文献

[1] Gao, G., Bai, D., Li, T., Li, J., Jia, Y., Li, J., et al. (2025) Understanding Filamentous Cyanobacteria and Their Adaptive Niches in Lake Honghu, a Shallow Eutrophic Lake. Journal of Environmental Sciences, 152, 219-234. [Google Scholar] [CrossRef] [PubMed]
[2] Fang, H., Wu, T., Ma, S., Miao, Y. and Wang, X. (2025) Biogenic Emission as a Potential Source of Atmospheric Aromatic Hydrocarbons: Insights from a Cyanobacterial Bloom-Occurring Eutrophic Lake. Journal of Environmental Sciences, 151, 497-504. [Google Scholar] [CrossRef] [PubMed]
[3] Liu, X. and Lou, Y. (2010) Global Dynamics of a Predator-Prey Model. Journal of Mathematical Analysis and Applications, 371, 323-340. [Google Scholar] [CrossRef] 
[4] Lotka, A.J. (1925) Elements of Physical Biology. Nature, 116, 461-461. [Google Scholar] [CrossRef] 
[5] Volterra, V. (1926) Fluctuations in the Abundance of a Species Considered Mathematically1. Nature, 118, 558-560. [Google Scholar] [CrossRef] 
[6] Yao, Y. and Liu, L. (2024) Dynamics of a Predator-Prey System with Foraging Facilitation and Group Defense. Communications in Nonlinear Science and Numerical Simulation, 138, Article 108198. [Google Scholar] [CrossRef] 
[7] Thirthar, A.A., Panja, P., Majeed, S.J. and Nisar, K.S. (2024) Dynamic Interactions in a Two-Species Model of the Mammalian Predator-Prey System: The Influence of Allee Effects, Prey Refuge, Water Resources, and Moonlights. Partial Differential Equations in Applied Mathematics, 11, Article 100865. [Google Scholar] [CrossRef] 
[8] Li, Y., He, M. and Li, Z. (2022) Dynamics of a Ratio-Dependent Leslie-Gower Predator-Prey Model with Allee Effect and Fear Effect. Mathematics and Computers in Simulation, 201, 417-439. [Google Scholar] [CrossRef] 
[9] Das, D., Kar, T.K. and Pal, D. (2023) The Impact of Invasive Species on Some Ecological Services in a Harvested Predator-Prey System. Mathematics and Computers in Simulation, 212, 66-90. [Google Scholar] [CrossRef] 
[10] Guin, L.N., Djilali, S. and Chakravarty, S. (2021) Cross-Diffusion-Driven Instability in an Interacting Species Model with Prey Refuge. Chaos, Solitons & Fractals, 153, Article 111501. [Google Scholar] [CrossRef] 
[11] Leslie, P.H. (1948) Some Further Notes on the Use of Matrices in Population Mathematics. Biometrika, 35, 213-245. [Google Scholar] [CrossRef] 
[12] Leslie, P.H. (1958) A Stochastic Model for Studying the Properties of Certain Biological Systems by Numerical Methods. Biometrika, 45, 16-31. [Google Scholar] [CrossRef] 
[13] Korobeinikov, A. (2001) A Lyapunov Function for Leslie-Gower Predator-Prey Models. Applied Mathematics Letters, 14, 697-699. [Google Scholar] [CrossRef] 
[14] Holling, C.S. (1965) The Functional Response of Predators to Prey Density and Its Role in Mimicry and Population Regulation. Memoirs of the Entomological Society of Canada, 97, 5-60. [Google Scholar] [CrossRef] 
[15] Allee, W.C., Park, O., Emerson, A.E., et al. (1949) Principles of Animal Ecology. Saunders Co.
[16] Berec, L., Angulo, E. and Courchamp, F. (2007) Multiple Allee Effects and Population Management. Trends in Ecology & Evolution, 22, 185-191. [Google Scholar] [CrossRef] [PubMed]
[17] Stephens, P.A. and Sutherland, W.J. (1999) Consequences of the Allee Effect for Behaviour, Ecology and Conservation. Trends in Ecology & Evolution, 14, 401-405. [Google Scholar] [CrossRef] [PubMed]
[18] Cai, Y., Zhao, C., Wang, W. and Wang, J. (2015) Dynamics of a Leslie-Gower Predator-Prey Model with Additive Allee Effect. Applied Mathematical Modelling, 39, 2092-2106. [Google Scholar] [CrossRef] 
[19] Zanette, L.Y., White, A.F., Allen, M.C. and Clinchy, M. (2011) Perceived Predation Risk Reduces the Number of Offspring Songbirds Produce per Year. Science, 334, 1398-1401. [Google Scholar] [CrossRef] [PubMed]
[20] Elliott, K.H., Betini, G.S. and Norris, D.R. (2017) Fear Creates an Allee Effect: Experimental Evidence from Seasonal Populations. Proceedings of the Royal Society B: Biological Sciences, 284, Article 20170878. [Google Scholar] [CrossRef] [PubMed]
[21] Sasmal, S.K. (2018) Population Dynamics with Multiple Allee Effects Induced by Fear Factors—A Mathematical Study on Prey-Predator Interactions. Applied Mathematical Modelling, 64, 1-14. [Google Scholar] [CrossRef] 
[22] Pal, S., Pal, N., Samanta, S. and Chattopadhyay, J. (2019) Effect of Hunting Cooperation and Fear in a Predator-Prey Model. Ecological Complexity, 39, Article 100770. [Google Scholar] [CrossRef] 
[23] Panday, P., Pal, N., Samanta, S. and Chattopadhyay, J. (2018) Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Fear. International Journal of Bifurcation and Chaos, 28, Article 1850009. [Google Scholar] [CrossRef] 
[24] Cong, P., Fan, M. and Zou, X. (2021) Dynamics of a Three-Species Food Chain Model with Fear Effect. Communications in Nonlinear Science and Numerical Simulation, 99, Article 105809. [Google Scholar] [CrossRef] 
[25] Wang, X., Tan, Y., Cai, Y. and Wang, W. (2020) Impact of the Fear Effect on the Stability and Bifurcation of a Leslie-Gower Predator-Prey Model. International Journal of Bifurcation and Chaos, 30, Article 2050210. [Google Scholar] [CrossRef] 
[26] Wang, J., Cai, Y., Fu, S. and Wang, W. (2019) The Effect of the Fear Factor on the Dynamics of a Predator-Prey Model Incorporating the Prey Refuge. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29, Article 083109. [Google Scholar] [CrossRef] [PubMed]
[27] Zhang, Z.F., Ding, T.R., Hang, W.Z., et al. (1992) Qualitative Theory of Differential Equation. American Mathematical Society.
[28] Perko, L. (2001) Differential Equations and Dynamical Systems. Springer. [Google Scholar] [CrossRef] 

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