带有简化的Monod-Haldane 型的R-M捕食者-食饵模型的局部稳定性分析
Local Stability Analysis with Simplified Monod-Haldane R-M Predator-Prey Model
摘要:本文研究了带有简化的Monod-Haldane型的Rosenzweig-MacArthur捕食者-食饵模型。 首先利用Routh-Hurwitz判据讨论常微分方程模型所有平衡点的存在性和局部稳定性。然后分析在一定条件下,正平衡点 E 处产生Hopf分支。
Abstract:In this paper, Rosenzweig-MacArthur predator-prey model with simplified Monod- Haldane type is studied. Firstly, the existence and local stability of all equilibrium points of ordinary differential model are discussed. Then analyze that under certain conditions, Hopf branches are generated at the positive equilibrium E .
文章引用:宋晨霞, 杨亚飞. 带有简化的Monod-Haldane 型的R-M捕食者-食饵模型的局部稳定性分析[J]. 理论数学, 2021, 11(7): 1379-1388. https://doi.org/10.12677/PM.2021.117155

参考文献

[1] Murray, J.D. (2002) An Introduction. 3rd Edition, Springer, New York.
[2] Kelley, P., Kowalewski, M. and Hansen, T.A. (2003) Predator-Prey Interactions in the Fossil Record. Springer Science & Business Media, Berlin.
https://doi.org/10.1007/978-1-4615-0161-9
[3] Lima, S.L. (1998) Nonlethal Effects in the Ecology of Predator-Prey Interactions. BioScience, 48, 25-34.
https://doi.org/10.2307/1313225
[4] Gause, G.F. (1934) Experimental Analysis of Vito Volterra’s Mathematical Theory of the Struggle for Existence. Science, 79, 16-17.
https://doi.org/10.1126/science.79.2036.16-a
[5] Wu, W.J. and Liang, G.W. (1989) Review of Methods Fitting Holling Disk Equation. Natural Enemies of Insects, 11, 96-100.
[6] Rosenzweig, M.L. and MacArthur, R.H. (1963) Graphical Representation and Stability Con- ditions of Predator-Prey Interactions. The American Naturalist, 97, 209-223.
https://doi.org/10.1086/282272
[7] Smith, H.L. (2008) The Rosenzweig-MacArthur Predator-Prey Model. School of Mathematical and Statistical Sciences, Arizona State University, Phoenix.
[8] Gonzalez-Olivares, E. and Huincahue-Arcos, J. (2014) Double Allee Effects on Prey in a Modi- fied Rosenzweig-MacArthur Predator-Prey Model. In: Mastorakis, N. and Mladenov, V., Eds., Computational Problems in Engineering, Springer International Publishing, Cham, 105-119.
https://doi.org/10.1007/978-3-319-03967-1 9
[9] Almanza-Vasquez, E., Ortiz-Ortiz, R.D. and Marin-Ramirez, A.M. (2015) Bifurcations in the Dynamics of Rosenzweig-MacArthur Predator-Prey Model Considering Saturated Refuge for the Preys. Applied Mathematical Sciences, 9, 7475-7482.
https://doi.org/10.12988/ams.2015.510640
[10] Moustafa, M., Mohd, M.H., Ismail, A.I., et al. (2018) Dynamical Analysis of a Fractional-Order Rosenzweig-MacArthur Model Incorporating a Prey Refuge. Chaos, Solitons & Fractals, 109, 1-13.
https://doi.org/10.1016/j.chaos.2018.02.008
[11] Javidi, M. and Nyamoradi, N. (2013) Dynamic Analysis of a Fractional Order Prey-Predator Interaction with Harvesting. Applied Mathematical Modelling, 37, 8946-8956.
https://doi.org/10.1016/j.apm.2013.04.024
[12] Jeschke, J.M., Kopp, M. and Tollrian R. (2002) Predator Functional Responses: Discriminating between Handling and Digesting Prey. Ecological Monographs, 72, 95-112.
https://doi.org/10.1890/0012-9615(2002)072[0095:PFRDBH]2.0.CO;2
[13] Holling, C.S. (1965) The Functional Response of Predators to Prey Density and its Role in Mimicry and Population Regulation. The Memoirs of the Entomological Society of Canada, 97, 5-60.
https://doi.org/10.4039/entm9745fv
[14] Jia, J. and Wei, X. (2016) On the Stability and Hopf Bifurcation of a Predator-Prey Model. Advances in Difference Equations, 2016, Article No. 86.
https://doi.org/10.1186/s13662-016-0773-y
[15] Kru, N. and Lax, C. (2019) The Rosenzweig-MacArthur System via Reduction of an Individual Based Model. Journal of Mathematical Biology, 78, 413-439.
https://doi.org/10.1007/s00285-018-1278-y

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