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

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

An Interdisciplinary Journal

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

Volume 4, Number 1, 2001

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E.V. Doktorov and I.S. Kuten
Suppression of Timing Jitter for Optical Solitons in Fibers. pp. 1-5

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 Gordon-Haus (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, Gordon-Haus effect, fiber

E.V. Grigorieva
Instabilities of Periodic Orbits in Lasers with Oscillating Delayed Feedback. pp. 6-12

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 infinite-dimensional 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 Self-consistent Gibbs Distribution over Quasienergies. pp. 13-17

Summary: We analyze radiative interaction of two-level molecules in a thermal gas and find that their cooperative dynamics can result in the self-organization 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 mean-field approach. We find that the latter may appear, in principle, via not only the second-order, but also the first-order phase transition. However, the first-order 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 second-order 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
Self-Organization in Intelligent Multi-Agent Systems and Neural Networks. I. pp. 18-46

Summary: The overview is devoted to autonomous agents and multi-agent systems. Different definitions of agents are discussed, and main properties of agents are highlighted. The agent-based 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. Inter-agent 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 English-Like Language (RELL) and analysis of meanings with the help of generalized frames from wavelets analysis.
Key words: autonomous agents, multi-agent 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. 47-57

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 11-year solar cycle. Moreover, this method is appropriate for revealing longer cycles and forecasting the further solar activity during one and a half of 11-year cycle.
Key words: solar activity, singular spectrum analysis, 11-year solar cycle

V.B. Nemtsov and A.N. Kamluk
Generalized Dynamics of the Conformational Mobility in the DNA Molecule. pp. 58-63

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 double-stranded DNA conformational mobility describes an experiment and can be used for non-contradictory interpretation of the experimental data and description of the DNA conformational dynamics in low-frequency range.
Key words: conformational vibrations, force constants, dispersion curves

V.I. Kuvshinov and A.V. Kuzmin
Order-to-Chaos Transition in Su(2) Spatially Homogeneous Model Field System. pp. 64-66

Summary: Classical dynamics of SU(2) model gauge field system with Higgs fields is considered from the viewpoint of chaos in the presence of non-zero 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, Yang-Mills fields.

H. Leblond
Solitons in ferromagnets and the KdV Hierarchy. pp. 67-84

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 multi-time expansion. It is governed by all equations of the KdV Hierarchy. Major result of the paper is that the multi-scale 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 f0 Avalanche Hierarchy in the Bak-Sneppen Evolution Model. pp. 85-89

Summary: For the Bak-Sneppen evolution model we present two master equations prescribing hierarchical structures of undercritical f0 avalanches and overcritical ones respectively. Taylor expansions of the master equations generate two infinite series of exact equations. Solutions of the two first-leading-order 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: self-organized criticality, evolution model, master equation, undercritical avalanches, over-critical 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. 90-93

Summary: Possibility of the forming of chaotic laser oscillation series using directly modulated laser diodes with two asymmetric quantum-well 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 power-current 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 non-periodic 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
Time-Delay Study of Earth Orientation Parameters at Inter-Annual Time Scales. pp. 94-105

Summary: We proceed to a reanalysis of time series of the Earth Orientation Parameters available from IERS [4] using Takens time-delay embedding technique [5]. Focusing on intermediate time scales rather than short ones as done in [3], we extract oscillations corresponding to Chandler wobble by singular-value decomposition [7] of the time-series of the Celestial Ephemeris Pole position (PMX,PMY) on the period 1890-2000. A Pi phase-shift of the oscillation around 1930 is pointed out explicitly. A similar study of the length-of-day time series shows strong correlation with indices measuring the strength of the ENSO phenomenon on the period 1962-1999 [23]. Differences between the dynamical systems approach and conventional signal analyses are emphasized.
Key words: time series, Earth Orientation Parameters, Takens time-delay embedding technique, ENSO phenomenon

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Designed and maintained by Dr. Nikolai N. Kostyukovich. Last updated: September 12, 2001
Created with assistance of Dr. Leonid F. Babichev
Copyright © 2001 The National Academy of Sciences of Belarus
Copyright © 2001 The Nonlinear Phenomena in Complex Systems