Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.4
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Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.4

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal
Published by The "Education and Upbringing" Publishing Company, Minsk, Republic of Belarus

Volume 2, Number 4, 1999
CONTENTS
Yu.L . Klimontovich
Entropy, Information, and Criteria of Order in Open Systems. pp. 125
Summary: Entropy, information and relative criteria of order for states of open systems are considered. In
the theory of communication two definitions of concept "information" are known. One of them coincides in form
with the Boltzmann entropy. The second definition of information is defined as the difference between unconditional and
conditional entropies. In the present work the latter is used for the definition of information about states of open systems with
various meanings of controlling (governing) parameter. Two kinds of open systems are considered. Those systems belong to
the first kind that with zero value of controling parameter are in the equilibrium state. The information about the equilibrium
state is equal to zero. During selforganization in the process of removal from the equilibrium state the information is
increased. For open systems of this class the conservation law for the sum of information and entropy with all values of
controlling parameter is proved. In open systems of the second class the equilibrium is
impossible. For them the concept ''norm of chaoticity '' is introduced. It allows to consider two kinds of selforganization
processes and to give the corresponding definitions of information. The treatment is carried out on a number (classical and quantum)
of examples of physical systems. The example of a medicobiological system is also considered.
P.C. Hendry, P.V.E. McClintock
Cosmological experiments in liquid helium. pp. 2635
Summary: Fast passage through a continuous phase transition is expected to result in the creation of topical
defects via the Kibble mechanism. Recent experiments involving the expansion of a small volume of liquid ^{4}He through
the lambda (superfluid) transition, as a model of the GUT (grand unified theory) symmetrybreaking transition of the early
universe, are discussed and set in context. Copious creation of quantized vortices, analogous to cosmic strings, is expected but
not observed. The possibility of developing a more sensitive version of the experiment is considered.
A. Cenys, A.Tamasevicius, G. Mykolaitis, A. Namajunas
Hyperchaos with High Metric Entropy. pp. 3640
Summary: A new design of the hyperchaotic systems with arbitrarily highnumber of positive Lyapunov
exponents is suggested. It exploits asa linear subsystem chain of harmonic oscillators corresponding tohighpass filter. In the new
design characteristic frequency ofthe system is increasing proportionally to the number of identicallinear elements. As a
result both number of the positive Lyapunov exponents and metric entropy increase when identical linearelements are added to the
system.
K. G. Kyritsi, L. Gallos, A. N. Anagnostopoulos, A. Cenys, G. L. Bleris
Chaotic Photoconductivity. pp. 4147
Summary: In modern optoelectronics, light sensors are playing a main role. The present work examines the
conditions of their performance, concerning photoconductivity. The model of a ntype photosensitive semiconductor containing two
localized levels in its energy gap is considered. The semiconductor is illuminated homogeneously with bandgaplight and
a constant electric field is applied. Electrons are excited by the illumination from the valence to the conductionband and by
the electric field from the localized levels to the conductionband. Electrons are also recombining from the
conduction to the valenceband and from the conductionband to the localized levels. Depending on the parameters of the system
(i.e. generation and recombination rates, electric field strength, capture and reemissioncoefficients of the levels,
ambient temperature, etc) the semiconductor is exhibiting periodic or chaotic conductivity. Different routes to chaos were
observed in this system, like period doubling, intermittency and crisis induced intermittency.
Yu. Andreyev, A. Dmitriev, A. Ovsyannikov
Chaotic processors and contentbased search of information in unstructured data bases. pp. 4853
Summary: In this report, we discuss an approach to construction of information searching systems based
on dynamic chaos and intended to operate in computer networks, local area or Internet. Also we discuss an application of this
technology to the problems of searching for information in unstructured text databases with naturallanguage requests.
T.A. King, W. Hogervorst, N.S. Kazak, V.A. Tugbaev, V.N.Belyi, N.A.Khilo, A.A.Ryzhevich
Investigation of properties of nonlinear optical frequencyconversion and parametric interactions using Bessel nondiffracting light beams. pp. 5460
Summary: The fundamental possibility of the formation of higherorder Bessel light beams is confirmed. The
transformation of beam order is observed when propagating circularly polarized light along the optical axis of biaxial
crystal under conditions of internal conical refraction. Theoretical and experimental investigations were made of the
characteristic features of frequency doubling of Bessel light beams by the oee interaction in a KTP crystal. All possible
vector and scalar interactions of planewave components of Bessel beams were observed experimentally. Parametric generation of
light by pumping with Bessel light beams is considered. A theory of azimuthmatched nonlinear interaction of Bessel light beams is developed.
A. Antonevich
The Schroedinger operator with dpotential: Finitedimensional perturbations approach. pp. 6171
Summary: The lecture presents the results on approximations of the Schroedinger operator with dpotential by means of approximations of the operator of multiplication by a d  function by
families of finite range operators. The resolvents behaviour is investigated and the resonance cases when the limit operator does
not coincide with the Laplace operator are singled out.
S. Ya. Kilin, D. B. Horoshko
Quantum theory of photodetection in the presence of feedback. pp. 7277
Summary: We develop a theory of photodetection in the presence of feedback valid for arbitrary time delay in the
feedback loop and any degree of field fluctuation. As a result we obtain an expression for the inloop photocurrent autocorrelation
function which differs from the traditional one by replacing the deltafunction by the Green function of the feedback loop. We
discuss two main consequences of the new formula: frequencydependent standard quantum limit in the presence of feedback, and the violation of statistical equivalence between
the photon flux and the photocurrent in the feedback loop.
A. Ruffing, D. Heim, C. Dingwall, U. Pforzheimer, B. Lampe
Revising moment problems of polarized densities in quantum chromodynamics. pp. 7888
Summary: The sensititivity of various future polarization experiments to the
first moment ?g of the polarized gluon density is elucidated in detail. It is shown to what extent the first moment can be
extracted from the future data as compared to the higher moments. We concentrate on two processes which in the near future will
become an important source of information on the polarized gluon density, namely the photoproduction of open charm to be studied
at CERN (COMPASS) and SLAC and the production of direct photons at RHIC.
M.A.Britch
Mathematical modelling of intracellular calcium signal transduction. pp. 8992
Summary: Two problems concerning intracellular regulating processes are considered. 1. Calcium wave propagation
taking into account cooperative action of two distinct classes of calcium channels. Such a system appear to exibit a wide variety
of spatialtemporal patterns including calcium oscillations with different periods coexhisting in different space regions. 2. The
system of reactions is proposed possessing the resonans property with respect to alternating modulation by externel factor. Such a
processes may serve as a mechanism of frequensyselective cellular response.
A. D. Linkevich
Representation of information in dynamical systems: measures, entropy and fractals. pp. 93104
Summary: An approach is suggested in which information encoding and information processing are implemented
through Borel measures supported on spaces associated with neural networks. To develop tools to read out pieces of information
stored in the system, the functional integration method is exploited. A special emphasis is put on fractal sets and fractal measures.
I.V. Babushkin, Yu.A. Logvin, and N.A. Loiko
Stationary and nonstationary symmetrybreaking optical patterns in a resonant bilayer. pp. 105110
Summary: Optical pattern formation is studied in a system consisting of two identical thin layers of resonance
medium illuminated by light fields of equal intensity from both sides. It is shown that transverse optical patterns emerged in
the system may be either symmetrical (identical for both layers) or symmetrybreaking. The influence of the interlayer mistuning
(distance between the layers) on the type of instability is elucidated. When delay effects are taken into account, a
relationship between the symmetrybreaking, bistability and the HopfIkeda transverse instabilities is revealed.
Designed and maintained by Dr. Nikolai N. Kostyukovich. Last updated: January 11, 2000
Created with assistance of Dr. Leonid F. Babichev
Copyright © 2000 The National Academy of Sciences of Belarus
Copyright © 1999 The Nonlinear Phenomena in Complex Systems