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Nonlinear Phenomena in Complex Systems, 2001, Vol.4, No.1

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

Volume 4, Number 1, 2001
CONTENTS
E.V. Doktorov and I.S. Kuten
Suppression of Timing Jitter for Optical Solitons in Fibers. pp. 15
Summary: We demonstrate on the examples of the Manakov and modified nonlinear
Schrödinger (MNSE) solitons that there exists a possibility to vary the
magnitude of the GordonHaus (GH) jitter by adjusting the soliton
parameters. While for the Manakov soliton we can reduce the GH jitter in one
of the polarization modes at the cost of the other mode, for MNSE soliton
the absolute suppression is possible.
Key words: soliton, birefringence, GordonHaus effect, fiber
E.V. Grigorieva
Instabilities of Periodic Orbits in Lasers with Oscillating Delayed Feedback. pp. 612
Summary: Finite dimensional maps are analytically derived for class B laser systems
with an incoherent external feedback. On the base of such maps, hierarchies
of periodic solutions of various structures are demonstrated in an
infinitedimensional delayed system. Sets of initial conditions and
parameters are determined for every type of the solutions. Bifurcations
induced by an oscillating delay are described.
Key words: delayed feedback, lasers, asymptotic analysis
V.V. Kocharovsky, Vl.V. Kocharovsky, and V.A. Kukushkin
Antiferroelectric Phase Transition in a Thermal Gas and Selfconsistent Gibbs Distribution over Quasienergies. pp. 1317
Summary: We analyze radiative interaction of twolevel molecules in a thermal gas and
find that their cooperative dynamics can result in the selforganization of
molecular dipole moments, i.e., the spontaneous formation of a static
polarization structure. Within quasiclassical consideration of translational
motion of molecules in the local field of the corresponding transverse
polarization wave, it is shown that actual energy levels of a single
molecule coincide with its quasienergies, which are well known in quantum
optics. This allows us to formulate a generalized Gibbs distribution over
quasienergy states of molecules and to apply it for investigation of the
statistical properties and specific features of the antiferroelectric phase
in the meanfield approach. We find that the latter may appear, in
principle, via not only the secondorder, but also the firstorder phase
transition. However, the firstorder one is weak and exists in a rather
narrow range of parameters because it is caused by a small group of
molecules taking part in the resonance interaction with the polarization
wave. The effect of the secondorder antiferroelectric phase transition is
owing to the collective interaction of the greater part of molecules and
therefore takes place under less exotic conditions, which seem to be
realizable experimentally.
Key words: cooperative phenomena, mean field approach, quasienergy states,
Gibbs distribution, antiferroelectric phase transition
Alexander D. Linkevich
SelfOrganization in Intelligent MultiAgent Systems and Neural Networks. I. pp. 1846
Summary: The overview is devoted to autonomous agents and multiagent systems.
Different definitions of agents are discussed, and main properties of agents
are highlighted. The agentbased computing is considered as a software
engineering paradigm, and areas of its applications are mentioned. Most
popular approaches to the theoretical description of agents are presented.
Interagent communication is discussed including the speech act theory,
Knowledge Sharing Effort (KSE), FIPA Agent Communication Language as well as
two ways toward communication through natural language: the Regularized
EnglishLike Language (RELL) and analysis of meanings with the help of generalized frames from wavelets analysis.
Key words: autonomous agents, multiagent systems, software engineering,
artificial intelligence, complex systems, communication, language, meaning, generalized frames
A. Loskutov, I.A. Istomin, K.M. Kuzanyan, and O.L. Kotlyarov
Testing and Forecasting the Time Series of the Solar Activity by Singular Spectrum Analysis. pp. 4757
Summary: To study and forecast the solar activity data a quite perspective method of
singular spectrum analysis (SSA) is proposed. As known, data of the solar
activity are usually presented via the Wolf numbers associated with the
effective amount of the sunspots. The advantages and disadvantages of SSA
are described by its application to the series of the Wolf numbers. It is
shown that the SSA method provides a sufficiently high reliability in the
description of the 11year solar cycle. Moreover, this method is appropriate for revealing longer cycles and forecasting the further solar activity during one and a half of 11year cycle.
Key words: solar activity, singular spectrum analysis, 11year solar cycle
V.B. Nemtsov and A.N. Kamluk
Generalized Dynamics of the Conformational Mobility in the DNA Molecule. pp. 5863
Summary: The proposed dynamic model of conformational mobility in DNA macromolecules
is a generalization of the models used to study conformational vibrations
and conformational transition dynamics, as a longitudinal component in this
model is taken additionally into account. For quantitative estimation of the
obtained results (for the calculation of a force constant) we used the DNA
macromolecule elastic model in the form of two twisted springs inserted into
each other. As a result the analysis, the dispersion curves for the
generalized model of DNA macromolecules have been obtained. Thus, the
offered model of the doublestranded DNA conformational mobility describes
an experiment and can be used for noncontradictory interpretation of the experimental data and description of the DNA conformational dynamics in lowfrequency range.
Key words: conformational vibrations, force constants, dispersion curves
V.I. Kuvshinov and A.V. Kuzmin
OrdertoChaos Transition in Su(2) Spatially Homogeneous Model Field System. pp. 6466
Summary: Classical dynamics of SU(2) model gauge field system with Higgs fields is
considered from the viewpoint of chaos in the presence of nonzero vacuum expectation value of Higgs fields. Conclusion that Higgs fields lead classical gauge fields to order is made.
Key words: chaos, stochastic dynamics, Higgs vacuum, YangMills fields.
H. Leblond
Solitons in ferromagnets and the KdV Hierarchy. pp. 6784
Summary: The higher order terms in the perturbative expansion that describes KdV
solitons propagation in ferromagnetic materials are considered. They satisfy
inhomogeneous linearized KdV equations, explicitly written down. The parity
and homogeneity properties of the expansion show that half of these
equations admit a zero solution. Long time propagation is investigated, through the consideration of the unbounded or secular solutions and a
multitime expansion. It is governed by all equations of the KdV Hierarchy. Major result of the paper is that the multiscale expansion can be achieved
up to any order with all its terms bounded, what is a necessary condition for its convergence.
Key words: KdV Hierarchy, Higher order KdV, KdV solitons, ferromagnets
W. Li and X. Cai
Description of Undercritical and Overcritical f_{0} Avalanche Hierarchy in the BakSneppen Evolution Model. pp. 8589
Summary: For the BakSneppen evolution model we present two master equations
prescribing hierarchical structures of undercritical f_{0} avalanches and
overcritical ones respectively. Taylor expansions of the master equations
generate two infinite series of exact equations. Solutions of the two
firstleadingorder equations yield two universal exponents: gamma, for "gamma" equation, and beta, for "beta" equation. It is found that gamma and
beta are each determined by a scaling function, related to the
configurations of the system. It is also shown that both gamma and beta equal 1 as the critical state is reached.
Key words: selforganized criticality, evolution model, master equation,
undercritical avalanches, overcritical avalanches, scaling function
L.I. Burov, V.K. Kononenko, M.I. Kramar, and G.I. Ryabtsev
Control of Dynamic Behavior in the Bistable Region of Laser Diodes. pp. 9093
Summary: Possibility of the forming of chaotic laser oscillation series using
directly modulated laser diodes with two asymmetric quantumwell active
layers has been demonstrated. The main feature of such chaotic regime is setting a modulation mean current within the hysteresis region of the laser
diode powercurrent characteristic with harmonic modulation amplitudes being adjusted to two hysteresis threshold current values. Numerical calculations
were made for 1.55 µm InGaAsP/InP laser diodes and condition of lasing the nonperiodic pulse series was obtained. It was shown that characteristics of
these series greatly depend on the modulation amplitude and mean current values.
Key words: laser diodes, quantum well, chaos, hysteresis, modulation
P. Manneville
TimeDelay Study of Earth Orientation Parameters at InterAnnual Time Scales. pp. 94105
Summary: We proceed to a reanalysis of time series of the Earth Orientation
Parameters available from IERS [4] using Takens timedelay embedding
technique [5]. Focusing on intermediate time scales rather than short ones as done in [3], we extract oscillations corresponding to Chandler wobble by
singularvalue decomposition [7] of the timeseries of the Celestial Ephemeris Pole position (PMX,PMY) on the period 18902000. A Pi phaseshift
of the oscillation around 1930 is pointed out explicitly. A similar study of the lengthofday time series shows strong correlation with indices
measuring the strength of the ENSO phenomenon on the period 19621999 [23].
Differences between the dynamical systems approach and conventional signal analyses are emphasized.
Key words: time series, Earth Orientation Parameters, Takens timedelay embedding technique, ENSO phenomenon