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]]. | ||
| − | The related field of study is known as dynamical systems. | + | The related field of study is known as '''dynamical systems'''. |
== Examples == | == Examples == | ||
| Line 24: | Line 24: | ||
* [[Attractor]] | * [[Attractor]] | ||
| + | * [[Behavioral modeling]] | ||
* [[Cantor tree surface]] | * [[Cantor tree surface]] | ||
* [[Chaos theory]] | * [[Chaos theory]] | ||
| + | * [[Cognitive modeling]] | ||
| + | * [[Dynamical systems theory]] | ||
* [[Excitable medium]] | * [[Excitable medium]] | ||
| + | * [[Feedback passivation]] | ||
* [[Geometrical space]] | * [[Geometrical space]] | ||
* [[Geometry]] | * [[Geometry]] | ||
| + | * [[Hamiltonian system]] | ||
* [[Hénon-Heiles System]] | * [[Hénon-Heiles System]] | ||
| + | * [[Infinite compositions of analytic functions]] | ||
| + | * [[Initial condition]] | ||
| + | * [[List of dynamical system topics]] | ||
* [[Mathematics]] | * [[Mathematics]] | ||
| + | * [[Oscillation]] | ||
| + | * [[People in systems and control]] | ||
| + | * [[Phase space]] | ||
| + | * [[Principle of maximum caliber]] | ||
* [[Strange attractor]] | * [[Strange attractor]] | ||
| + | * [[Sharkovskii's theorem]] | ||
| + | * [[System dynamics]] | ||
| + | * [[Systems theory]] | ||
* [[Time]] | * [[Time]] | ||
Latest revision as of 07:43, 14 October 2016
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
- Behavioral modeling
- Cantor tree surface
- Chaos theory
- Cognitive modeling
- Dynamical systems theory
- Excitable medium
- Feedback passivation
- Geometrical space
- Geometry
- Hamiltonian system
- Hénon-Heiles System
- Infinite compositions of analytic functions
- Initial condition
- List of dynamical system topics
- Mathematics
- Oscillation
- People in systems and control
- Phase space
- Principle of maximum caliber
- Strange attractor
- Sharkovskii's theorem
- System dynamics
- Systems theory
- Time
External links
- Dynamical systems @ Wikipedia
