What does dynamical system mean?
Definitions for dynamical system
dy·nam·i·cal sys·tem
This dictionary definitions page includes all the possible meanings, example usage and translations of the word dynamical system.
Princeton's WordNet
dynamical systemnoun
(physics) a phase space together with a transformation of that space
Wiktionary
dynamical systemnoun
A mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space.
Wikipedia
Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometrical manifold. The evolution rule of the dynamical system is a function that describes what future states follow from the current state. Often the function is deterministic, that is, for a given time interval only one future state follows from the current state. However, some systems are stochastic, in that random events also affect the evolution of the state variables. In physics, a dynamical system is described as a "particle or ensemble of particles whose state varies over time and thus obeys differential equations involving time derivatives". In order to make a prediction about the system's future behavior, an analytical solution of such equations or their integration over time through computer simulation is realized. The study of dynamical systems is the focus of dynamical systems theory, which has applications to a wide variety of fields such as mathematics, physics, biology, chemistry, engineering, economics, history, and medicine. Dynamical systems are a fundamental part of chaos theory, logistic map dynamics, bifurcation theory, the self-assembly and self-organization processes, and the edge of chaos concept.
ChatGPT
dynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models are used to describe the behavior of many real-world systems such as the movement of planets or the behavior of electronic circuits. This can be defined by ordinary differential equations for continuous time or by difference equations for discrete time. The rule is deterministic, meaning that for a given point in time only one next state is possible.
Wikidata
Dynamical system
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 that can be represented by a point in an appropriate state space. 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.
Matched Categories
Numerology
Chaldean Numerology
The numerical value of dynamical system in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of dynamical system in Pythagorean Numerology is: 3
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"dynamical system." Definitions.net. STANDS4 LLC, 2024. Web. 24 Apr. 2024. <https://www.definitions.net/definition/dynamical+system>.
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