By Ludmilla A. Uvarova, Arkadii E. Arinstein, Anatolii V. Latyshev
ISBN-10: 1461371740
ISBN-13: 9781461371748
ISBN-10: 1461547997
ISBN-13: 9781461547990
The articles during this publication are derived from the 3rd overseas convention of a similar identify, held June 29-July three, 1998. issues contain: nonlinear exaltations in condensed structures, evolution of complicated platforms, dynamics and constitution of molecular and biomolecular structures, mathematical versions of move tactics in nonlinear structures and numerical modeling and algorithms.
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Additional info for Mathematical Models of Non-Linear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media
Sample text
These parameters may be considered as "passport data" of the dynamic system under consideration. The second set of the dimensional parameters has a meaning of the components of the Kolmogorov K-entropy. Usually, the Kolmogorov entropyl,2 is considered as a scalar. In our approach, the introduced parameters characterize the rates of losing information which depends on the type of the "color- non-regularities". These parameters may differ for different types of non-regularities. We call the developed approach to time series analysis flicker-noise spectroscopy (FNS)6-8.
Figure 14. The logarithms of module of continuous wavelet transform coefficients (with Mexican hat as a mother wavelet) for the time series No 25. Each next fragment of this map is the one forth in area of the previous picture. The horizontal coordinate is the time (in dimensionless units). The vertical coordinate corresponds to the values of the wavelet scales (in dimensionless units). Grayscale (legend on the top) reflects logarithm of absolute values of wavelet coefficients. Time series is shown over the maps.
Coefficients squares correspond to energy at the given time scale and at the given time moment. So displayed wavelet map characterizes energy redistribution dynamics in the system at the evolution expressed by "full" time series (Fig. la). There is manifested hierarchy structure in such maps that is reproduced on different time scales. Branching points in the wavelet map correspond to scale splitting up. Presented by wavelet maps structure that cbaracterized the energy redistribution in the system and reproduced on different scales point to certain correlation of studied membrane potential fluctuations and can be characterized by fractal dimension determined from 13 dependence of local extremes number on scale magnitude.
Mathematical Models of Non-Linear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media by Ludmilla A. Uvarova, Arkadii E. Arinstein, Anatolii V. Latyshev
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