Autonomous system (mathematics)

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.

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.

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.

  1. ^ Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis Accessed 10 October 2019.