# Article

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Keywords:
delay differential equation; equilibrium; convergence
Summary:
Consider the delay differential equation $\dot{x}(t)=g(x(t),x(t-r)), \qquad \mathrm{(1)}$ where $r>0$ is a constant and $g\:\mathbb{R}^2\rightarrow \mathbb{R}$ is Lipschitzian. It is shown that if $r$ is small, then the solutions of (1) have the same convergence properties as the solutions of the ordinary differential equation obtained from (1) by ignoring the delay.
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