Delay differential equation: Difference between revisions

Revision as of 15:49, 8 July 2012

Definition

The notion of delay differential equation (abbreviated DDE) is a variant of the notion of differential equation (in other words, delay differential equations are not (ordinary) differential equations). If we denote the dependent variable by $x$ and the independent variable by $t$ (Which we think of as time), the first-order first-degree case is:

$\frac{d x (t)}{d t} = f (t, x (t), the entire trajectory of x prior to time t)$

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 ==Definition==
-The notion of '''delay differential equation''' (abbreviated '''DDE''') is a variant of the notion of [[differential equation]] (in other words, delay differential equations are not (ordinary) differential equations). If we denote the dependent variable by <math>x</math> and the independent variable by <math>t</math>, the first-order first-degree case is:
+The notion of '''delay differential equation''' (abbreviated '''DDE''') is a variant of the notion of [[differential equation]] (in other words, delay differential equations are not (ordinary) differential equations). If we denote the dependent variable by <math>x</math> and the independent variable by <math>t</math> (Which we think of as time), the first-order first-degree case is:
 <math>\frac{dx(t)}{dt} = f(t,x(t),\mbox{the entire trajectory of } x \mbox{ prior to time } t)</math>