Abstract

A STUDY OF LYAPUNOV STABILITY ANALYSIS OF SOME THIRD ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATION

Ozioko, Luke Arinze and Omeike, Mathew O.

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Abstract Lyapunov functions enable analyzing the stability of dynamic systems described by ordinary differential equations without finding the solution of such equations. Stability is one of the properties of solutions of any differential equation. A dynamical system in a state of equilibrium is said to be stable. In other words, a system has to be in a stable state before it can be asymptotically stable which means that stability does not necessarily imply asymptotic stability but asymptotic stability implies stability. For nonlinear systems, devising a Lyapunov function is not an easy task to solve in general. In this paper, we construct a suitable Lyapunov functions for some third order non-linear ordinary differential equations. We present three possible Lyapunov functions by finding quadratic form function for the appropriate third order linear differential equation, and construct Lyapunov functions for some non-linear ordinary differential equations by analogy with the linear system. Keywords: Lyapunov function, Asymptotic Stability, Linear ODE, Nonlinear ODE, Third Order ODE. 1. Introduction Lyapunov functions ar

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