The construction and application of Lyapunov function

The Lyapunov second method is the most common in the reaearch of the stability of differential equation solutions,by using this method,the key point is to construct Lyapunov Function,namely,V Function.This paper aims to analyze and summarize the relative theories about the Lyapunov Second Methods of systematic stability and how to determine the stability of system with Lyapunov Function.In the Lotka-Voltera Models and the Epidemiological Models including SIR and SI models,we determine directly the stability under equilibrium state through constructing the Lyapunov Function(a function related to ln),as well as applying to Lyapunov Function and symbol characteristic of derivative.