Ads
related to: discrete dynamical systems pdf file viewer free
Search results
Results from the WOW.Com Content Network
There are many forms of these maps, [2] many of which are equivalent under a coordinate transformation. For example two of the most common ones are: : +: The second one can be mapped to the first using the fact that . = + (), so : + is the same under the transformation = + ().
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]
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.
For discrete dynamical systems, consider the system + = (,). Then a local bifurcation occurs at (,) if the matrix , has an eigenvalue with modulus equal to one. If the eigenvalue is equal to one, the bifurcation is either a saddle-node (often called fold bifurcation in maps), transcritical or pitchfork bifurcation.
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 .
A Markov partition in mathematics is a tool used in dynamical systems theory, allowing the methods of symbolic dynamics to be applied to the study of hyperbolic dynamics.By using a Markov partition, the system can be made to resemble a discrete-time Markov process, with the long-term dynamical characteristics of the system represented as a Markov shift.
An update scheme specifying the mechanism by which the mapping of individual vertex states is carried out so as to induce a discrete dynamical system with map F: K n → K n. The phase space associated to a dynamical system with map F: K n → K n is the finite directed graph with vertex set K n and directed edges (x, F(x)).
Ads
related to: discrete dynamical systems pdf file viewer free