Asymptotic Stability of Singular OrdinaryDifferential Equation Established ViaExtendedSystem Reduction | ||
| JOURNAL OF THI-QAR SCIENCE | ||
| Article 1, Volume 5, Issue 1, March 2016, Pages 43-47 | ||
| Author | ||
| Kamal H. Yasir | ||
| Abstract | ||
| In this paper we discuss the stability of an equilibrium solution of ODE effected bythe extended system reduction. The main conclusion of this paper is that, under thehypothesis rank(DF)_((y_0,0) )=n-1, the stability or instability of an equilibrium solution (y_0,0) of y ̇=F(y,α) is determined by the sign of DG where G is the reduced function obtained by the extended system reduction. Also the stability of a small amplitude periodic solution of ordinary differential equation y ̇=F(y,α) is discussed by the same way. | ||
| Keywords | ||
| Singular ordinary differential equation; Asymptotic stability; Extended system reduction | ||
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