Author(s)

R. N. Okereke

Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria.

This paper is concerned with the stability analysis of nonlinear third order ordinary differential equations of the form . We construct a suitable Lyapunov function for this purpose and show that it guarantees asymptotic stability. Our approach is to first consider the linear version of the above ODE, by taking and study its Lyapunov stability. Exploiting the similarities between linear and nonlinear ODE, we construct a Lyapunov function for the stability analysis of the given nonlinear differential equation.

Nonlinear ODE, Energy, Lyapunov Function, Assymptotic Stability

Okereke, R. (2016) Lyapunov Stability Analysis of Certain Third Order Nonlinear Differential Equations. Applied Mathematics, 7, 1971-1977. doi: 10.4236/am.2016.716161.