# Space-Modeled Dynamic System

(Redirected from dynamical systems)

A Space-Modeled Dynamic System is a dynamic system that can be modeled by a mathematical space (such as a metric space).

**See:**Deterministic System (Mathematics), Attractor Point, Function (Mathematics), Manifold, Mathematical Model, State (Controls), Real Numbers, Vector Space, Point (Geometry), State Space.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Dynamical_system Retrieved:2015-7-25.
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**dynamical system**is a concept in mathematics where a fixed rule describes how a point in a geometrical space depends on time. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.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.^{[1]}^{[2]}

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