# autonomous system

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 $\dot{x}_{n+1}=1$.

 Title autonomous system Canonical name AutonomousSystem Date of creation 2013-03-22 13:37:26 Last modified on 2013-03-22 13:37:26 Owner Daume (40) Last modified by Daume (40) Numerical id 6 Author Daume (40) Entry type Definition Classification msc 34A99 Synonym autonomous Synonym autonomous equation Synonym nonautonomous Synonym nonautonomous equation Related topic TimeInvariant Related topic SystemDefinitions Defines nonautonomous system