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Zbl 1016.34076
Pituk, Mihály
Convergence to equilibria in a differential equation with small delay. (English)
[J] Math. Bohem. 127, No.2, 293-299 (2002). ISSN 0862-7959

Summary: Consider the delay differential equation $$ \dot x(t)=g(x(t),x(t-r)),\tag 1 $$ where $r>0$ is a constant and $g :\bbfR ^2\rightarrow \bbfR $ is Lipschitzian. It is shown that if $r$ is small, then the solutions to (1) have the same convergence properties as the solutions to the ordinary differential equation derived from (1) by ignoring the delay.

MSC 2000:: *34K25 Asymptotic theory of functional-differential equations
34K12 Properties of solutions of functional-differential equations

Keywords: delay differential equation; equilibrium; convergence

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