具有Holling III功能反应函数的种群表观竞争模型的动力学分析
Dynamical Analysis of an Apparent Competition Model among Populations with Holling III Functional Response
摘要: 本文研究了一类具有Holling III功能反应函数的种群表观竞争模型的动力学分析，其中包含一个捕食者和两个猎物种群。首先，运用一般的代数求解法，得到了系统零平衡点、边界平衡点及正平衡点(双猎物–捕食者共存)的存在条件与解析表达式；其次，运用线性化方法和Routh-Hurwitz判据，得出了系统不同平衡点的局部渐近稳定性。最后，通过数值模拟验证了在特定参数条件下，一个猎物种群可通过间接效应导致另一猎物种群局部灭绝。
Abstract: In this paper, dynamical analysis of an apparent competition model among populations with Holling III functional response, which consists of one predator and two prey populations, is studied. Firstly, general algebraic methods are used to obtain the existence conditions and explicit expressions for the zero equilibrium, boundary equilibria, and the positive equilibrium (where both prey species coexist with the predator) of the model. Then, by employing the linearization method and the Routh-Hurwitz criterion, the local asymptotic stability of the model’s different equilibria is derived. Finally, through numerical simulations, it is verified that the local extinction of one prey species by another prey species via indirect effects can be induced under specific parameter conditions.
文章引用：闫文艳, 王琳蓉, 雷诗艺. 具有Holling III功能反应函数的种群表观竞争模型的动力学分析[J]. 应用数学进展, 2026, 15(8): 12-26. https://doi.org/10.12677/aam.2026.158329

参考文献

[1] Holt, R.D. and Polis, G.A. (1997) A Theoretical Framework for Intraguild Predation. The American Naturalist, 149, 745-764.
https://doi.org/10.1086/286018
[2] Schmitz, O.J. (2007) Predator Diversity and Trophic Interactions. Ecology, 88, 2415-2426.
https://doi.org/10.1890/06-0937.1
[3] Holt, R.D. (1977) Predation, Apparent Competition, and the Structure of Prey Communities. Theoretical Population Biology, 12, 197-229.
https://doi.org/10.1016/0040-5809(77)90042-9
[4] Holt, R.D. and Bonsall, M.B. (2017) Apparent Competition. Annual Review of Ecology, Evolution, and Systematics, 48, 447-471.
https://doi.org/10.1146/annurev-ecolsys-110316-022628
[5] Chailleux, A., Mohl, E.K., Teixeira Alves, M., Messelink, G.J. and Desneux, N. (2014) Natural Enemy‐Mediated Indirect Interactions among Prey Species: Potential for Enhancing Biocontrol Services in Agroecosystems. Pest Management Science, 70, 1769-1779.
https://doi.org/10.1002/ps.3916
[6] Chaneton, E.J. and Bonsall, M.B. (2000) Enemy‐Mediated Apparent Competition: Empirical Patterns and the Evidence. Oikos, 88, 380-394.
https://doi.org/10.1034/j.1600-0706.2000.880217.x
[7] 巴雷, 李志坚, 杨雪茹. 植物种群表观竞争机制及其研究进展[J]. 生态学报, 2023, 43(13): 5281-5288.
[8] Lou, Y., Tao, W. and Wang, Z. (2025) Effects and Biological Consequences of the Predator-Mediated Apparent Competition I: ODE Models. Journal of Mathematical Biology, 91, Article No. 47.
https://doi.org/10.1007/s00285-025-02286-x
[9] Abrams, P.A. (1999) Is Predator-Mediated Coexistence Possible Inunstable Systems? Ecology, 80, 608-621.
https://doi.org/10.1890/0012-9658(1999)080[0608:ipmcpi]2.0.co;2
[10] Hsu, S.B. (1981) Predator-Mediated Coexistence and Extinction. Mathematical Biosciences, 54, 231-248.
https://doi.org/10.1016/0025-5564(81)90088-2
[11] Piltz, S.H., Veerman, F., Maini, P.K. and Porter, M.A. (2017) A Predator—2 Prey Fast—Slow Dynamical System for Rapid Predator Evolution. SIAM Journal on Applied Dynamical Systems, 16, 54-90.
https://doi.org/10.1137/16m1068426
[12] 张剑. 具有收获率的捕食与被捕食系统的定性分析[D]: [硕士学位论文]. 哈尔滨: 哈尔滨理工大学, 2005.
[13] 赵玉凤, 刘桂荣. 一类随机捕食系统的平稳分布及其概率密度函数[J]. 山东大学学报(理学版), 2024, 59(10): 74-88.
[14] Wu, Z., Wang, Z., Cai, Y., Yin, H. and Wang, W. (2025) Pattern Formation in a Fractional-Order Reaction-Diffusion Predator-Prey Model with Holling-III Functional Response. Advances in Continuous and Discrete Models, 29, 1-18.
https://doi.org/10.1186/s13662-025-03891-2
[15] 孙书荣, 韩振来, 张超. 常微分方程[M]. 济南: 山东大学出版社, 2019.
[16] 林风光. 具有阶段结构的生态流行病模型的定性分析及最优收获问题[J]. 陕西理工大学学报(自然科学版), 2023, 39(4):76-82.

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