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Lyapunov Stability Analysis of Certain Third Order Nonlinear Differential Equations
Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria
- 1 Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria
Applied Mathematics·Volume 07 (2016)·Pages 1971–1977·Published 14 October 2016·DOI10.4236/am.2016.716161
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Abstract
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.
KeywordsNonlinear ODEEnergyLyapunov FunctionAssymptotic Stability
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