An analysis on the stability of a state dependent delay differential equation

Abstract

In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term τ(u(t))=a+bu(t)c+bu(t).$\tau (u(t)) = \frac{{a + bu(t)}}{{c + bu(t)}}.$ Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.

Keywords

• asymptotic stability
• state depended delay
• delay differential equation
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