Dynamical Systems

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Dynamical Systems

A system of equations where the output of one equation is part of the input for another. A simple version of a dynamical system is linear simultaneous equations. Non-linear simultaneous equations are nonlinear dynamical systems.

Dynamical Systems

A series of equations in which the output of one becomes the input of another. One equation may determine a company's earnings for a particular period. The earnings, then, may be put into another equation to determine the earnings per share. This is a simple example of dynamical systems. It may (and often does) include a long string of equations.
References in periodicals archive ?
The theory in [9] shows that every dynamical system of order one can be prolonged to an Euler-Lagrange dynamical system of order two whose trajectories are geodesies of a Lagrangian defined by the velocity vector field (Lagrange structure of order one).
The time derivative of V along the trajectory of the error dynamical system (2) is as follows
that is, the cone of nonnegative vectors, and consider the dynamical system
Section 2 provides the necessary background information on the invariance and conserved quantities of dynamical system and especially the Noether's theorem.
Truth be told, the derivation of a dynamical system from the payoff matrix of the underlying game is tricky business.
17] The dynamical system is said to converge to the solution set [K.
Despite this sensitivity, however, chaotic trajectories in a given dynamical system still generally end up on an attractor that has a particular geometry -- albeit one that can look extremely convoluted and complicated.
This volume contains 15 selected papers discussing connections between fractal geometry and dynamical system in pure mathematics and connections between these two and other fields of mathematics.
The term "chaos" refers to situations in which the behavior of a dynamical system -- whether a pendulum or a collection of gravitationally interacting bodies -- depends sensitively on initial conditions.
Recurring Themes and Applications: Important themes and applications, such as dynamical system formulation, phase portraits, linearization, stability of equilibrium solutions, vibrating systems, and frequency response are revisited and reexamined in different applications and mathematical settings.
To predict the future course of a dynamical system such as a swinging pendulum, physicists have traditionally counted on solving a suitable equation to find a formula describing the system's position or state at any time.

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