基于广义Lyapunov方法的植物传染病模型的全局动力学
Global Dynamics for a Plant Disease Model Based on Generalized Lyapunov Approach
摘要: 本文研究了按比率p移除易感植株为控制措施的一类Lotka-Volterra Filippov型植物传染病模型。讨论了无病平衡点和地方病平衡点的存在性和稳定性以及伪焦点的存在性。通过构造合适的非光滑的Lyapunov函数利用广义Lyapunov方法研究该模型在不同经济阈值下的全局动力学，得到三个结果。
Abstract: In this paper, a Lotka-Volterra Filippov plant infectious disease model was studied with the removal of susceptible plants at a ratio of p as control measure. The existence and stability of disease-free equilibrium and endemic equilibrium and the existence of false focus were discussed. By constructing appropriate non-smooth Lyapunov functions and using the generalized Lyapunov method, the global dynamics of the model under different economic thresholds were studied, and three results were obtained.
文章引用：冷轩, 陈会敏. 基于广义Lyapunov方法的植物传染病模型的全局动力学[J]. 应用数学进展, 2021, 10(4): 1086-1095. https://doi.org/10.12677/AAM.2021.104117

参考文献

[1] Jeger, M.J., Van Den Bosch, F. and Madden, L.V. (1998) A Model for Analysing Plant-Virus Transmission Characteristics and Epidemic Development. Mathematical Medicine and Biology: A Journal of the IMA, 15, 1-18. [Google Scholar] [CrossRef] 
[2] Fishman, S., Marcus, R. and Talpaz, H. (1983) Epidemiological and Economic Models for Spread and Control of Citrus Tristeza Virus Disease. Phytoparasitica, 11, 39-49. [Google Scholar] [CrossRef] 
[3] Jones, R.A.C. (2000) Determining ‘Threshold’ Levels for Seed-Borne Virus Infection in Seed Stocks. Virus Research, 71, 171-183. [Google Scholar] [CrossRef] 
[4] Chan, M.S. and Jeger, M.J. (1994) An Analytical Model of Plant Virus Disease Dynamics with Roguing and Replanting. Journal of Applied Ecology, 31, 413-427. [Google Scholar] [CrossRef] 
[5] van den Bosch, F. and de Roos, A.M. (1996) The Dynamics of Infectious Diseases in Orchards with Roguing and Replanting as Control Strategy. Journal of Mathematical Biology, 35, 129-157. [Google Scholar] [CrossRef] 
[6] Zhao, T. and Xiao, Y. (2013) Non-Smooth Plant Disease Models with Economic Thresholds. Mathematical Biosciences, 241, 34-48. [Google Scholar] [CrossRef] [PubMed]
[7] Wang, J., Zhang, F. and Wang, L. (2016) Equilibrium, Pseudoequilibrium and Sliding-Mode Heteroclinic Orbit in a Filippov-Type Plant Disease Model. Nonlinear Analysis: Real World Applications, 31, 308-324. [Google Scholar] [CrossRef] 
[8] Filippov, A.F. (2013) Differential Equations with Discontinuous Right Hand Sides: Control Systems. Springer Science & Business Media, Berlin.
[9] 黄立宏, 郭振远, 王佳伏. 右端不连续微分方程理论与应用[M]. 北京: 科学出版社, 2011.
[10] Bacciotti, A. and Ceragioli, F. (1999) Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions. ESAIM: Control, Optimisation and Calculus of Variations, 4, 361-376. [Google Scholar] [CrossRef] 
[11] Clarke, F.H. (1990) Optimization and Nonsmooth Analysis. Society for Industrial and Applied Mathematics, New York.
[12] Forti, M., Grazzini, M. and Nistri, P. (2006) Generalized Lyapunov Approach for Convergence of Neural Networks with Discontinuous or Non-Lipschitz Activations. Physica D: Nonlinear Phenomena, 214, 88-99. [Google Scholar] [CrossRef] 

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