Editing Autonomous system (mathematics) (section)

== Definition ==

An '''autonomous system''' is a [[system of ordinary differential equation]]s of the form
<math display="block">\frac{d}{dt}x(t)=f(x(t))</math>
where {{mvar|x}} takes values in {{mvar|n}}-dimensional [[Euclidean space]]; {{mvar|t}} is often interpreted as time.

It is distinguished from systems of differential equations of the form
<math display="block">\frac{d}{dt}x(t)=g(x(t),t)</math>
in which the law governing the evolution of the system does not depend solely on the system's current state but also the parameter {{mvar|t}}, again often interpreted as time; such systems are by definition not autonomous.