Difference between revisions of "Dynamical system"
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| − | In [[mathematics]], a '''dynamical system''' is a concept where a fixed rule describes how a point in a geometrical space depends on time. | + | In [[mathematics]], a '''dynamical system''' is a concept where a fixed rule describes how a point in a [[geometrical space]] depends on [[time]]. |
== Examples == | == Examples == | ||
| Line 23: | Line 23: | ||
* [[Attractor]] | * [[Attractor]] | ||
* [[Chaos theory]] | * [[Chaos theory]] | ||
| + | * [[Geometrical space]] | ||
| + | * [[Geometry]] | ||
* [[Mathematics]] | * [[Mathematics]] | ||
* [[Strange attractor]] | * [[Strange attractor]] | ||
| + | * [[Time]] | ||
== External links == | == External links == | ||
* [https://en.wikipedia.org/wiki/Dynamical_system Dynamical systems] @ Wikipedia | * [https://en.wikipedia.org/wiki/Dynamical_system Dynamical systems] @ Wikipedia | ||
Revision as of 20:17, 17 February 2016
In mathematics, a dynamical system is a concept where a fixed rule describes how a point in a geometrical space depends on time.
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
External links
- Dynamical systems @ Wikipedia
