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Download as PDF; Printable version ... In control engineering, a discrete-event dynamic system (DEDS) is a ... and Control of Logical Discrete Event Systems.
From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called discrete dynamical systems.
A discrete dynamical system, discrete-time dynamical system is a tuple (T, M, Φ), where M is a manifold locally diffeomorphic to a Banach space, and Φ is a function. When T is taken to be the integers, it is a cascade or a map. If T is restricted to the non-negative integers we call the system a semi-cascade. [14]
Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions . Chaotic maps often occur in the study of dynamical systems .
Download as PDF; Printable version ... In the theory of dynamical systems, the exponential map can be used as the evolution function of the discrete nonlinear ...
The concept of fixed points is of primary importance in discrete dynamical systems. Another graphical technique that can be used for one-variable mappings is the spider web projection. After determining an initial value x 0 {\displaystyle x_{0}} on the horizontal axis, draw a vertical line from the initial value x 0 {\displaystyle x_{0}} to the ...
In mathematics, symbolic dynamics is the study of dynamical systems defined on a discrete space consisting of infinite sequences of abstract symbols. The evolution of the dynamical system is defined as a simple shift of the sequence. Because of their explicit, discrete nature, such systems are often relatively easy to characterize and understand.
A period-halving bifurcation occurs when a system switches to a new behavior with half the period of the original system. A period-doubling cascade is an infinite sequence of period-doubling bifurcations. Such cascades are a common route by which dynamical systems develop chaos. [1] In hydrodynamics, they are one of the possible routes to ...