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:
“I have no concern with any economic criticisms of the communist system; I cannot enquire into whether the abolition of private property is expedient or advantageous. But I am able to recognize that the psychological premises on which the system is based are an untenable illusion. In abolishing private property we deprive the human love of aggression of one of its instruments ... but we have in no way altered the differences in power and influence which are misused by aggressiveness.”
—Sigmund Freud (1856–1939)