autonomous system


A system of ordinary differential equation is autonomousMathworldPlanetmath when it does not depend on time (does not depend on the independent variable) i.e. 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. 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 𝐱˙=𝐟(𝐱,t) 𝐱n then it can be written as an autonomous system with 𝐱n+1 and by doing a substitution with xn+1=t and 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