Application of Lyapunov Functions to some nonlinear third order differential equations

Abstract

Lyapunov functions were initiated by a Russian Mathematician Alexander, M. Lyapunov. It is a generalization based on the well-known observation that near the equilibrium point of a physical system, the total energy of agiven system is either constant or decreasing. So the idea here is to introduce some functions now known as Lyapunov functions which generalize the total energy of a system. This paper centers on how to obtain Lyapunov functions for nonlinear thirdorder systems and their applications.