Dynamical system

In mathematics, a dynamical system is a concept where a fixed rule describes how a point in a geometrical space depends on time.

The related field of study is known as dynamical systems.

Examples

Examples include mathematical models which describe:

• The swinging of a clock pendulum
• The flow of water in a pipe
• The number of fish each springtime in a lake

Description

At any given time a dynamical system has a state given by a set of real numbers (a vector) that can be represented by a point in an appropriate state space (a geometrical manifold).

Small changes in the state of the system create small changes in the numbers.

The evolution rule of the dynamical system is a fixed rule that describes what future states follow from the current state.

The rule is deterministic; in other words, for a given time interval only one future state follows from the current state.

See also

• Attractor
• Cantor tree surface
• Chaos theory
• Excitable medium
• Geometrical space
• Geometry
• Hénon-Heiles System
• Mathematics
• Strange attractor
• Time

External links

• Dynamical systems @ Wikipedia