PlanetMath: autonomous system

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autonomous system

(Definition)

A system of ordinary differential equation is autonomous when it does not depend on time (does not depend on the independent variable) i.e. $\dot{x}=f(x)$ . In contrast nonautonomous is when the system of ordinary differential equation does depend on time (does depend on the independent variable) i.e. $\dot{x}=f(x,t)$ .

It can be noted that every nonautonomous system can be converted to an autonomous system by adding a dimension. i.e. If $\dot{\textbf{x}}=\textbf{f}(\textbf{x},t)$ $\textbf{x} \in \mathbb{R}^n$ then it can be written as an autonomous system with $\textbf{x} \in \mathbb{R}^{n+1}$ and by doing a substitution with $x_{n+1} = t$ and $\dot{x}_{n+1}=1$ .

"autonomous system" is owned by Daume.

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Other names:

autonomous, autonomous equation, nonautonomous, nonautonomous equation

Also defines:

nonautonomous system

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Cross-references: dimension, variable, independent, ordinary differential equation
There are 11 references to this entry.

This is version 3 of autonomous system, born on 2003-05-09, modified 2006-07-21.
Object id is 4260, canonical name is AutonomousSystem.
Accessed 11140 times total.

Classification:

AMS MSC:

34A99 (Ordinary differential equations :: General theory :: Miscellaneous)

Pending Errata and Addenda

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