系数含有时滞的种群模型的动力学分析
Dynamic Analysis of Population Models with Time-Delay Coefficients
DOI: 10.12677/AAM.2022.115335, PDF,    科研立项经费支持
作者: 沈 维*, 姚佳佳, 范宏卓：兰州交通大学数学系，甘肃 兰州
关键词: 种群模型；稳定性；成熟时滞；Hopf分支；Population Model； Stability； Mature Time Delay； Hopf Bifurcation
摘要: 考虑系数含有成熟离散时滞的种群模型。通过分析相应特征方程的根在复平面上的分布，研究了模型平衡点的稳定性与Hopf分支。最后利用Matlab软件包对相应的理论结果进行了数值验证。
Abstract: A population model with mature discrete time delays is considered. The stability of the equilibrium point and the Hopf branch of the model are studied by analyzing the distribution of the roots of the corresponding characteristic equation on the complex plane. Finally, the corresponding theoretical results are verified by Matlab software package.
文章引用：沈维, 姚佳佳, 范宏卓. 系数含有时滞的种群模型的动力学分析[J]. 应用数学进展, 2022, 11(5): 3164-3174. https://doi.org/10.12677/AAM.2022.115335

参考文献

[1] Jiang, Z.C. and Zhang, W.Z. (2010) Bifurcation Analysis in Single-Species Population Model with Delay. Science China Mathematics, 53, 1475-1481. [Google Scholar] [CrossRef] 
[2] Nicholson, A.J. (1954) Compensa-tory Reactions of Populations to Stresses, and Their Evolutionary Significance. Australian Journal of Zoology, 2, 1-8. [Google Scholar] [CrossRef] 
[3] Gurney, M.S., Blythe, S.P. and Nisbee, R.M. (1980) Nicholson’s Blow-flies Revisited. Nature, 287, 17-21. [Google Scholar] [CrossRef] 
[4] Shu, H.Y., Wang, L. and Wu, J.H. (2013) Global Dynamics of Nicholson’s Blowflies Equation Revisited: Onset and Termination of Nonlinear Oscillations. Journal of Differential Equations, 255, 2565-2586. [Google Scholar] [CrossRef] 
[5] Beretta, E. (2016) Discrete or Distributed Delay? Effects on Stability of Population Growth. Mathematical Biosciences and Engineering, 13, 19-41. [Google Scholar] [CrossRef] [PubMed]
[6] Wang, S.F., Tang, H.P. and Ma, Z.H. (2021) Hopf Bifurcation of a Multiple-Delayed Predator-Prey System with Habitat Complexity. Mathematics and Computers in Simulation, 180, 1-23. [Google Scholar] [CrossRef] 
[7] Meng, X.Y., Huo, H.F. and Zhang, X.B. (2011) Stability and Global Hopf Bifurcation in a Delayed Food Web Consisting of a Prey and Two Predators. Communications in Nonlinear Science and Numerical Simulation, 16, 4335-4348. [Google Scholar] [CrossRef] 
[8] Song, Y.L., Han, M.A. and Wei, J.J. (2005) Stability and Hopf Bifurcation Analysis on a Simplified BAM Neural Network with Delays. Physica D: Nonlinear Phenomena, 200, 185-204. [Google Scholar] [CrossRef] 
[9] 沈维, 姚佳佳. 具有收获率和Holling-II型功能反应函数的时滞系统的定性分析[J]. 内江师范学院学报, 2021, 36(10): 36-41.
[10] 沈维. 时滞双向联想记忆神经网络模型的稳定性与Hopf分支[J]. 内江师范学院学报, 2020, 35(12): 27-31.
[11] Yan, X.P. and Li, W.T. (2007) Bifur-cation and Global Periodic Solutions in a Delayed Facultative Mutualism System. Physica D: Nonlinear Phenomena, 227, 51-69. [Google Scholar] [CrossRef] 

为你推荐