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In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior.Maps may be parameterized by a discrete-time or a continuous-time parameter.
The Band and Band-Raman calculations assume that the M shell may contribute to internal conversion to a non-negligible extent, and incorporates a general term (called "N+") which takes into account the small effect of any higher shells there may be, while the Rösel calculation works like the Band, but does not assume that all shells contribute ...
Polynomial chaos (PC), also called polynomial chaos expansion (PCE) and Wiener chaos expansion, is a method for representing a random variable in terms of a polynomial function of other random variables. The polynomials are chosen to be orthogonal with respect to the joint probability distribution of these random variables.
These subregions are called bands. When there are multiple bands, the orbit moves through each band in a regular order, but the values within each band are irregular. Such chaotic orbits are called band chaos or periodic chaos, and chaos with k bands is called k -band chaos. Two-band chaos lies in the range 3.590 < r < 3.675, approximately.
Folded-towel map attractor. A hyperchaotic system is a dynamical system with a bounded attractor set, on which there are at least two positive Lyapunov exponents. [1]Since on an attractor, the sum of Lyapunov exponents is non-positive, there must be at least one negative Lyapunov exponent.
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Number of atoms N = Number of atoms remaining at time t. N 0 = Initial number of atoms at time t = 0
Quantum chaos is the field of physics attempting to bridge the theories of quantum mechanics and classical mechanics. The figure shows the main ideas running in each direction. Quantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory.
He and his colleagues (Edward Ott and Celso Grebogi) had shown with a numerical example that one can convert a chaotic motion into a periodic one by a proper time-dependent perturbation of the parameter. This article is considered a classic among the works in the control theory of chaos, and their control method is known as the O.G.Y. method.