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 the time, they are also named Time-invariant system.
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 and, using very weak assumptions, a dynamical system can be transformed into an autonomous system.
Read more about Autonomous System (mathematics): Definition, Properties, Example, Qualitative Analysis, Solution Techniques
Famous quotes containing the words autonomous and/or system:
“There is a totalitarian regime inside every one of us. We are ruled by a ruthless politburo which sets ours norms and drives us from one five-year plan to another. The autonomous individual who has to justify his existence by his own efforts is in eternal bondage to himself.”
—Eric Hoffer (1902–1983)
“He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one.”
—Henry David Thoreau (1817–1862)