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:
“Justice in the hands of the powerful is merely a governing system like any other. Why call it justice? Let us rather call it injustice, but of a sly effective order, based entirely on cruel knowledge of the resistance of the weak, their capacity for pain, humiliation and misery. Injustice sustained at the exact degree of necessary tension to turn the cogs of the huge machine-for- the-making-of-rich-men, without bursting the boiler.”
—Georges Bernanos (1888–1948)