理论(学习稳定性)
李雅普诺夫函数
应用数学
数学
Volterra方程
李雅普诺夫指数
控制理论(社会学)
计量经济学
计算机科学
非线性系统
物理
控制(管理)
量子力学
机器学习
人工智能
标识
DOI:10.1016/j.chaos.2012.03.009
摘要
In this paper, we study the global dynamics of a class of mathematical epidemiological models formulated by systems of differential equations. These models involve both human population and environmental component(s) and constitute high-dimensional nonlinear autonomous systems, for which the global asymptotic stability of the endemic equilibria has been a major challenge in analyzing the dynamics. By incorporating the theory of Volterra–Lyapunov stable matrices into the classical method of Lyapunov functions, we present an approach for global stability analysis and obtain new results on some three- and four-dimensional model systems. In addition, we conduct numerical simulation to verify the analytical results.
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