A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. 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.
Read more about Dynamical System: Overview, Basic Definitions, Linear Dynamical Systems, Local Dynamics, Bifurcation Theory, Ergodic Systems, Multidimensional Generalization
Famous quotes containing the word system:
“New York is more now than the sum of its people and buildings. It makes sense only as a mechanical intelligence, a transporter system for the daily absorbing and nightly redeploying of the human multitudes whose services it requires.”
—Peter Conrad (b. 1948)