Autonomous system (mathematics)

In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable. When the variable is time, they are also called time-invariant systems.

Stability diagram classifying Poincaré maps of linear autonomous system as stable or unstable according to their features. Stability generally increases to the left of the diagram.[1] Some sink, source or node are equilibrium points.
2-dimensional case refers to Phase plane.

Many laws in physics, where the independent variable is usually assumed to be time, are expressed as autonomous systems because it is assumed the laws of nature which hold now are identical to those for any point in the past or future.

Autonomous systems are closely related to dynamical systems. Any autonomous system can be transformed into a dynamical system[citation needed] and, using very weak assumptions[citation needed], a dynamical system can be transformed into an autonomous system[citation needed].