TYPES OF LYAPUNOV FUNCTIONS AND GLOBAL STABILITY

Abstract

The stability analysis of dynamical systems is a critical aspect of understanding their behavior and ensuring reliable performance in various applications. Lyapunov functions play a pivotal role in this analysis, offering a powerful mathematical tool to assess the stability of equilibrium points. Despite the fact that at the moment there is no general method for finding the Lyapunov function, this review explores the diverse landscape of Lyapunov functions and their contributions to achieving global stability in dynamical systems. Examples of epidemic models and their Lyapunov functions with the graphical implementations in Python in different reproduction numbers are included for deeper understanding. In addition, the history of the Lyapunov global asymptotic stability theorem was considered shortly. Possible further research ideas in this area are included at the end.