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# Autonomous system

In differential equations, an autonomous system is an equation of the form
$\frac{d}{dt}x(t)=f(x(t))$
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
$\frac{d}{dt}x(t)=g(x(t),t)$
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.

In the Internet, an autonomous system (AS for short) is a collection of IP networks under control of a single entity, typically an internet provider with redundant networking connections.

Unique AS numbers are allocated to each AS for use in BGP routing. The numbers are assigned by the same authorities that allocate IP addresses. AS numbers are currently 16-bit integers. There are public numbers which may be used on the Internet and range from 1 to 64511 and private numbers from 64512 to 65535 which can be used within an organisation.

Types of AS:

• Multihomed AS
• Stub AS
• Transit AS

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