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Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.1

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Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.1

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

Published by The "Education and Upbringing" Publishing Company, Minsk, Republic of Belarus

Volume 2, Number 1, 1999

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CONTENTS


M.I. Dykman, V.N. Smelyanskiy, D.G. Luchinsky, R. Mannella, P.V.E. McClintock, N.D. Stein
Fluctuations and irreversibility in nonequilibrium systems. pp. 1--7.

Summary: Large rare fluctuations in a nonequilibrium system are investigated theoretically and by analogue electronic experiment. It is emphasized that the optimal paths calculated via the eikonal approximation of the Fokker--Planck equation can be identified with the locus of the ridges of the prehistory probability distributions which can be calculated and measured experimentally for paths terminating at a given final point in configuration space. The pattern of optimal paths and its singularities, such as caustics, cusps and switching lines have been calculated and measured experimentally for a periodically driven overdamped oscillator, yielding results that are shown to be in good agreement with each other.

V. Kuvshinov, R. Shulyakovsky
Correlation moments behaviour as a new signal of QCD vacuum structure. pp. 8--13.

Summary: We calculate and analyse factorial, cumulant and Hq-moments in dependence on their rank q for the instanton-induced deep inelastic scattering in the frameworks of QCD taking into account both quark and gluon multiplicities.The obtained correlation moments behaviour has specific form, which can be considered as a new criterion of the QCD-instantons identification on experiment.

V.V. Belov, A.V. Kondratenko, V.B. Nemtsov
Surface properties of liquid crystals. pp. 14--17.

Summary: The integral equation for one-particle distribution function has been used to calculate the dependence of liquid crystal material coefficients on the distance from the wall.

D.V. Ushakov and V.K. Kononenko
Abnormal character of the diffusivity-mobility ratio in doping superlattices. pp. 18--23.

Summary: The influence of high level of doping in type n-i-p-i crystal structures on electron and hole state distributions is examined. Abnormal behaviour in the diffusivity-mobility ratio due to shortening of the density state tails under excitation of doping superlattices is described.

Alexander D. Linkevich
Thinking, language, self, and attractors: cognitive studies and synergetic paradigm. pp. 24--40.

Summary: It is considered how thinking may be imitated with the aid of neural networks. Manners of representation of information in mind and in neural networks are discussed. Links between language, thinking and other mental phenomena are examined. Self-conscious mind is treated as self-organization of neural activity. Some possible dynamical mechanisms of thinking are analysed.

S.I. Maximov
The production of human capital. A dynamic approach. pp. 41--49.

Summary: This article points a way getting a new model in the field. The model is drawn out from Ben-Porath's model well known, but differs much of its base concepts. Two key approaches are in the use in the article. First, the model is based on the concept of expectations. Second, the model is made of a wide use of dynamic approach. Combining these two techniques we have had the model, a remake of Ben-Porath's model, which is more a flexible one.

S.M. Karpuk, O.G. Romanov, A.L. Tolstik
Different types of bistability upon multiwave mixing in a nonlinear interferometer. pp. 50--55.

Summary: Interaction of light beams in nonlinear Fabry--Perot interferometer has been theoretically studied in conditions of rescattering from the diffraction dynamic structures formed in the medium volume. Consideration has been given to the scheme for the symmetric propagation of two light beams in the interferometer and the scheme for the normal incidence of a reference beam upon oblique incidence of the signal one. It has been demonstrated that one can realize optical bistability of the S-, N-, butterfly-type and, owing to the pitchfork bifurcation, asymmetric modes of bistability.

L.A. Kotomtseva, S.G. Rusov
Complex regular and chaotic regimes in a laser with a saturable absorber. pp. 56--59.

Summary: Some types of regular pulsation with jumps over several steady states and chaotic oscillations as a result of numerical simulations for a laser with a saturable absorber with two longitudinal modes are described.

L.I. Minchenko, T.V. Satsura
On the parametric differentiability of the optimal solutions in nonlinear programming. pp. 60--63.

Summary: There investigate differentiability properties of solutions of perturbed nonlinear programming problems under the condition of R-regularity.

L. Benet and T.H. Seligman
Characterization of the incoming asymptotes in the restricted three-body problem. pp. 64--67.

Summary: We consider the subset of initial conditions which result in trapped orbits for the circular Restricted Three-Body Problem as a function of the Jacobi integral, in the case of equal masses of the heavy bodies. We show that this set contributes in localizing the major bifurcations of the problem where the chaotic saddle changes abruptly, while it is not sufficient to distinguish between the hyperbolic or non-hyperbolic character of the chaotic saddle in finite precision measurements.

Maja Bracic and Aneta Stefanovska
Wavelet analysis in studying the dynamics of blood circulation. pp. 68--77.

Summary: The characteristic frequencies of human blood distribution system span over a wide frequency interval and also vary in time. To capture them the wavelet transform, a method of time-frequency analysis with frequency dependent time and frequencyre solution, was applied. Peaks at approximately the same frequencies were found in all measured signals related to the cardiovascular system revealing their common origin. Further, we hypothesise that peaks which appear at exactly the same frequencies in all signals measured from the one subject reflect the action of central regulatory mechanisms, whilst other have a local origin.

Alexander Rauh
Global stability of systems related to the Navier-Stokes equations. pp. 78--82.

Summary: A generalized Lyapunov method is outlined which predicts global stability of a broad class of dissipative dynamical systems. The method is applied to the complex Lorenz model and to the Navier--Stokes equations. In both cases one finds compact domains in phase space which contain the omega-sets of all trajectories, in particular the fixed points, limit cycles, and strange attractors.

S.V.Sergeyev, I.V.Brezgunova
Light polarization symmetry breaking in an anisotropic dye laser with a saturable absorberfor orthogonal dipole moments with emission and absorption. pp. 83--90.

Summary: Asymmetric steady states and auto-oscillations have been found and ways to chaos have been discussed for an anisotropic dye laser with a saturable absorber for the case of orthogonal dipoles with absorption and emission. Increasing the rate of Orientational Relaxationof excited molecules leads to further asymmetrization of solutions for small rates of Orientational Relaxation and to Polarization Symmetry Restoration into the form of symmetric auto-oscillations for high rates.

A.T. Vlassov
Multiplicative elements and deformations. pp. 91--99.

Summary: Multiplicative and bimultiplicative elements are generalizations of the well known concept of multiplicative matrix in a bialgebra. Deformations are connected with twisted multiplicative elements. Some problems for bialgebras and their actions, in the presence of multiplicative or bimultiplicative elements, are considered.

E.A. Nikiforov, R.M. Yulmetyev
Molecular transport in complex system. pp. 100--103.

Summary: The report contains results obtained by investigation of molecular transport phenomena in complex systems using the magnetic resonance spectroscopy method. Based on the taking into account the correlation memory and structure effects the kinetic theory of spin density fluctuations in condensed matters is presented. NMR, gamma and optic spectroscopy methods were used.

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