Autonomous System (mathematics)

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

Other articles related to "autonomous":

Autonomous System (mathematics) - Solution Techniques - Higher Orders
... is no analogous method for solving third- or higher-order autonomousequations ... This should not be surprising, considering that nonlinear autonomoussystems in three dimensions can produce truly chaotic behavior such as the Lorenz attractor and the Rössler attractor ... With this mentality, it also isn't too surprising that general non-autonomousequations of second order can't be solved explicitly, since these can also be chaotic (an example of this is a ...

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)

    We recognize caste in dogs because we rank ourselves by the familiar dog system, a ladderlike social arrangement wherein one individual outranks all others, the next outranks all but the first, and so on down the hierarchy. But the cat system is more like a wheel, with a high-ranking cat at the hub and the others arranged around the rim, all reluctantly acknowledging the superiority of the despot but not necessarily measuring themselves against one another.
    —Elizabeth Marshall Thomas. “Strong and Sensitive Cats,” Atlantic Monthly (July 1994)