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  • 1
    Language: English
    In: Chaos, Solitons and Fractals, Feb, 2014, Vol.59, p.35(7)
    Description: To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.chaos.2013.11.007 Byline: Lasko Basnarkov, Gregory S. Duane, Ljupco Kocarev Abstract: We study the synchronization of a coupled pair of one-dimensional Kuramoto-Sivashinsky systems, with equations augmented by a third-space-derivative term. With two different values of a system parameter, the two systems synchronize in the generalized sense. The phenomenon persists even in the extreme case when one of the equations is missing the extra term. Master-slave synchronization error is small, so the generalized synchronization relationship is useful for predicting the state of the master from that of the slave, or conversely, for controlling the slave. The spatial density of coupling points required to bring about generalized synchronization appears to be related to the wavelength of traveling wave solutions, and more generally to the width of coherent structures in the separate systems. Article History: Received 22 August 2013; Accepted 16 November 2013
    ISSN: 0960-0779
    Source: Cengage Learning, Inc.
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  • 2
    Language: English
    In: Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, February 2014, Vol.59, pp.35-41
    Description: We study the synchronization of a coupled pair of one-dimensional Kuramoto–Sivashinsky systems, with equations augmented by a third-space-derivative term. With two different values of a system parameter, the two systems synchronize in the generalized sense. The phenomenon persists even in the extreme case when one of the equations is missing the extra term. Master–slave synchronization error is small, so the generalized synchronization relationship is useful for predicting the state of the master from that of the slave, or conversely, for controlling the slave. The spatial density of coupling points required to bring about generalized synchronization appears to be related to the wavelength of traveling wave solutions, and more generally to the width of coherent structures in the separate systems.
    Keywords: Sciences (General) ; Mathematics
    ISSN: 0960-0779
    E-ISSN: 1873-2887
    Source: ScienceDirect Journals (Elsevier)
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  • 3
    Language: English
    In: Chaos, Solitons and Fractals, 2009, Vol.41(4), pp.2178-2192
    Description: This paper deals with state-dependent open Markovian (or exponential) queuing networks, for which arrival and service rates, as well as routing probabilities, may depend on the queue lengths. For a network of this kind, following Mandelbaum and Pats, we provide a formal definition of its associated fluid model, and we focus on the relationships which may occur between the network stochastic dynamics and the deterministic dynamics of its corresponding fluid model, particularly focusing on queuing networks whose fluid models have global periodic attractors.
    Keywords: Sciences (General) ; Mathematics
    ISSN: 0960-0779
    E-ISSN: 1873-2887
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  • 4
    Language: English
    In: Chaos, Solitons and Fractals, 2008, Vol.35(3), pp.562-577
    Description: Synchronization in random networks with given expected degree sequences is studied. We also investigate in details the synchronization in networks whose topology is described by classical random graphs, power-law random graphs and hybrid graphs when → ∞. In particular, we show that random graphs almost surely synchronize. We also show that adding small number of global edges to a local graph makes the corresponding hybrid graph to synchronize.
    Keywords: Sciences (General) ; Mathematics
    ISSN: 0960-0779
    E-ISSN: 1873-2887
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  • 5
    Language: English
    In: Chaos, Solitons and Fractals, 2003, Vol.15(2), pp.319-326
    Description: Chaotic pulse position modulation (CPPM) is a novel technique to communicate with chaotic signals based upon pulse trains in which the intervals between two pulses are determined by chaotic dynamics of a pulse generator. Using numerical simulations we show that CPPM offers excellent multi-path performance. We simulated the CPPM radio system, which is designed for a WLAN application and operates in the 2.4 GHz ISM frequency band with IEEE 802.11 compliant channel spacing. In this case, the average performance loss due the multi-path for CPPM is less than 5 dB.
    Keywords: Sciences (General) ; Mathematics
    ISSN: 0960-0779
    E-ISSN: 1873-2887
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  • 6
    Language: English
    In: Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, 01 August 1998, Vol.9(8), pp.1359-1366
    Description: Applications of Lie derivatives in chaos synchronization and localization of periodic orbits are discussed. We present examples illustrating how one can construct a system that synchronizes with a given dynamical system, and how one can find a set that contains all periodic orbits of a dynamical system.
    Keywords: Sciences (General) ; Mathematics
    ISSN: 0960-0779
    E-ISSN: 1873-2887
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  • 7
    Language: English
    In: Chaos, Solitons and Fractals, 1998, Vol.9(1), pp.283-293
    Description: The work deals with control of spatio-temporal chaos in coupled ordinary differential equations. We propose a method based on the following ideas: stabilization of unstable periodic orbits embedded in spatio-temporal chaos, perturbation of minimal number of system variables, and perturbation only at regular time intervals and, if possible, not of all coupled systems. Numerical examples are given for various spatially ordered phases.
    Keywords: Sciences (General) ; Mathematics
    ISSN: 0960-0779
    E-ISSN: 1873-2887
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