Autonomous system (mathematics)

In differential equations, an autonomous system is an equation of the form

<math>\frac{d}{dt}x(t)=f(x(t))<math>

where x takes values in n-dimensional Euclidean space and t is usually time. It is distinguished from systems of differential equations of the form

<math>\frac{d}{dt}x(t)=g(x(t),t)<math>

in which the law governing the rate of motion of a particle depends not only on the particle's location, but also on time; such systems are not autonomous.