Space-Modeled Dynamic System
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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.
- A 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]
- A 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.