Nonlinear Phenomena in Complex Systems, 1998, Vol.1, No.1

THE NATIONAL ACADEMY OF SCIENCES OF BELARUS

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

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

Volume 1, Number 1, 1998

Preface

M. Robnik
Topics in Quantum Chaos in Generic Systems. pp. 1--22.

Summary: We review the main ideas and results in the stationary problems of quantum chaos in generic (mixed) systems, whose classical dynamics has regular (invariant tori) and chaotic regions coexisting in the phase space. First we discuss the universality classes of spectral fluctuations (GOE/GUE for ergodic systems, and Poissonian for integrable systems). We explain the problems in the calculation of the invariant (Liouville) measure of classically chaotic components, which has recently been studied by Robnik et al (1997) and by Prosen and Robnik (1998). Then we describe the Berry--Robnik (1984) picture, which is claimed to become exact in the strict semiclassical limit h ® 0. However, at not sufficiently small values of h we see a crossover regime due to the localization properties of stationary quantum states where Brody-like behaviour with the fractional power law level repulsion is observed in the corresponding quantal energy spectra.

A. Cenys, A. Tamaseviius, A. Namajnas, G. Mykolaitis
Synchronization of Hyperchaos. pp. 23--27.

Summary: Synchronization of the hyperchaotic systems is investigated. The possibility to synchronize two identical hyperchaotic systems via only one dynamical variable is demonstrated. Obtained results are illustrated exploiting the Rössler hyperchaotic equations and electronic circuits exhibiting hyperchaotic behaviour.

G.S. Bokun, V.S. Vikhrenko, V.A. Zhuk, V.A. Tsurko
Quasichemical Approximation for Consolidation Site Transformation of Lattice Gas System. pp. 28--32.

Summary: The method for improvement of the quasichemical approximation is developed. The consolidated lattice consisted of complex sites that include all states of regular blocks of the initial lattice is introduced. Based on the quasichemical approximation on the consolidated lattice the expressions for thermodynamic functions and probabilities for occupation of lattice sites by particles are derived. Computations for the two-dimensional square lattice with attractive nearest neighbor interparticle interaction have shown the significant improvement of the results with increasing the block's size.

V.A. Gaisyonok, G.G.Krylov
Brusselator Model on SO(3) Group: Theory and Applications to Orientationally Sensitive Reactions. pp. 33--43.

Summary: The Brusselator model on S0(3) group space is proposed. Its applicability to the description of orientationally sensitive macromolecular reactions is discussed. The numerical simulations for the model in the simplest case of factorization, namely for S2/S1 homogeneous space have been fulfilled, absorption and fluorescence anisotropy kinetics has been obtained. Key words: nonlinear dynamics, distributed system, Brusselator model, macromolecule, orientational-relaxation. fluorescence, anisotropy.

H.V. Grushevskaja, A.T. Vlassov
Jet Dynamics in Brusselator System. pp. 45--54.

Summary: The asymptotic solution for Brusselator model has been constructed using geometrical reformulation of the problem. The method of decoupling of an infinite chain of the equations for jets has been proposed.

N.N. Rosanov
Localized Spatio-Temporal Structures in Bistable Nonlinear Optical Systems. pp. 55--61.

Summary: A review is given of localized structures of light which are generated in spatially distributed optical bistable systems promising for optical information processing. I compare main features of these dissipative soliton-like structures ("optical autosolitons") and of the traditional optical solitons in transparent media.

S.V. Sergeyev, L.V. Kondratieva
Undirectional Anisotropic Ring Cavity Laser's Polarization States. pp. 62--67.

Summary: Semiclassical model of unidirectional anisotropic ring cavity dye laser has been investigated analytically and numerically. Light-polarization states in the form of bistable circularly and elliptically polarized waves, alternative circularly and chaotically polarized waves have been found based on Poincare sphere approach.

A.V. Naumenko, N.A. Loiko, S.I.Turovets
Optimal Chaos Control in a Modulated Class-b Laser with Delayed Impulsive Feedback. pp. 68--75.

Summary: We analyze theoretically a chaos control scheme for a modulated class-B laser based on impulsive delayed feedback proposed by Bielawski, Derozier and Glorieux [Phys. Rev. A 47 (1993) R2492]. The detailed analytical and numerical studies of unstable manifold evolution in phase space are presented. The conditions for optimal control are elucidated.

V.S. Gurin, V.P. Poroshkov
Drift-Assisted Diffusion-Limited Aggregation in Two and Three Dimensions. pp. 76--79.

Summary: The model of fractal growth on the basis of the standard diffusion limited aggregation (DLA) of particles in two and three dimensions with the increased probability to move in the direction of the center of growth which Simulates an attraction effect is considered.

R.M. Yulmetyev, M.Ya. Kleiner.
Fractal Dynamics of the Long-Range Correlations in Short-Time Human Memory. pp. 80--91.

Summary: The problem of the description of temporal evolution of the random variables in terms of the information (Shannon) entropy of correlation processes has been considered. The influence and important role of the two mutually-dependent channels of the entropy alternation: correlation (creation or generation of correlations) and anti-correlation (decay or annihilation of correlation) have been discussed. The developed method has been used in the analysis of fractal kinetics of the long-range fluctuation in the short-time human memory.

L. Babichev
Structure of Superconducting Phase in Quasi-One-Dimensional High-Temperature Superconductors. pp. 92--95.

Summary: Numerical solutions of the generalized time-dependent Ginzburg-Landau (TDGL) equations for the "threshold perturbations" in the case of thermodynamic potential with two local minima are obtained for various values of decoupling factor F. Nonequilibrium processes for superconducting systems on the basis of the generalized TDGL equation are investigated. It is shown that the transition to the superconducting phase for current-carrying filaments is the first-order one both for infinitely long and for finite quasi-one-dimensional systems.

A.T. Vlassov
Parametric Interaction of Dynamical Systems with Inputs. pp. 96--104.

Summary: A general hierarchy of dynamical systems depended on parameters with additional structure on their phase space has been defined. The structure is a submersion with a vertical vector field and connection. The most important property of the geometrical structure is the possibility to introduce a natural fairly large class of interaction between such systems.

A.D. Linkevich
Some Fitzhugh-Like Neuronal Models. pp. 105--108.

Summary: A class of modifications of the FitzHugh model of neurons are proposed and studied. Time evolution of the neuron state is described by a system of M differential equations which are linear except for one nonlinear term taken to be a bounded function. Bounds of neuron phase trajectories are derived. Networks of neurons under consideration are investigated as well. The learning problem is formulated and reduced to a standard form. Sufficient conditions are found for retrieval of memorized patterns.

V.B. Nemtsov
Statistical Theory of the Elastic Properties of DNA Molecules. pp. 109--113.

Summary: Simple physical model is developed to study some characteristics of elastic properties of DNA molecules. We adapted the statistical theory of orientational elasticity of liquid crystals for description of the elastic properties of DNA molecule. The order of magnitude estimation of the elastic constants of DNA molecule is given and a new caloric effect due to the bending is predicted.

L. Babichev, D. Klenitsky, V. Kuvshmov, V. Shaporov, R. Shulyakovsky, N. Sinitsyn
Nonperturbative Effects of Quantum Chromodynamics. pp. 114--121.

Summary: Here we consider analytically the possibility of existence and correlation properties of three nonperturbative QCD phenomena: squeezed gluon states in jets, strong instanton in DIS and temperature hysteresis phenomenon in the first order QGP phase transitions.

Academy

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Copyright © 1998 The Nonlinear Phenomena in Complex Systems

Volume 1, Number 1, 1998

CONTENTS