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单词 AutonomousSystem
释义

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.

Titleautonomous system
Canonical nameAutonomousSystem
Date of creation2013-03-22 13:37:26
Last modified on2013-03-22 13:37:26
OwnerDaume (40)
Last modified byDaume (40)
Numerical id6
AuthorDaume (40)
Entry typeDefinition
Classificationmsc 34A99
Synonymautonomous
Synonymautonomous equation
Synonymnonautonomous
Synonymnonautonomous equation
Related topicTimeInvariant
Related topicSystemDefinitions
Definesnonautonomous system
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更新时间:2025/5/4 17:00:20