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 $\dot{\text{𝐱}}=\text{𝐟}(\text{𝐱},t)$ $\text{𝐱}\in {ℝ}^n$ then it can be written as an autonomous system with $\text{𝐱}\in {ℝ}^{n+1}$ 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