Geodesic
Convergence to equilibria in a differential equation with small delay
Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 293-299

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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.
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.
DOI : 10.21136/MB.2002.134154
Classification : 34K12, 34K25
Keywords: delay differential equation; equilibrium; convergence 
Pituk, Mihály. Convergence to equilibria in a differential equation with small delay. Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 293-299. doi: 10.21136/MB.2002.134154
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