New Conditions That Guarantee Uniform Asymptotically Stable and Absolute Stability of Singularly Perturbed Systems of Certain Class of Nonlinear Differential Equations
Ebiendele Peter *
Department of Basic Science, School of General Studies, Federal Polytechnic, Auchi, Edo State, Nigeria.
Asuelinmen Osoria
Department of Basic Science, School of General Studies, Federal Polytechnic, Auchi, Edo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The objectives of this paper is to investigate singularly perturbed system of the fourth order differential equations of the type, to establish the necessary and sufficient new conditions that guarantee, uniform asymptotically stable, and absolute stability of the system. The Liapunov’s functions were the mathematical model used to establish the main results of this study. The study was motivated by some authors in the literature, Grujic LJ.T, and Hoppensteadt, F., and the results obtained in this study improves upon their results to the case where more than two arguments was established.
Keywords: Uniform asymptotical stable, absolute stability, singularly perturbed, differential equations