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  • Conference paper
    Jadbabaie A, Motee N, Barahona M, 2005,

    On the stability of the Kuramoto model of coupled nonlinear oscillators

    , Pages: {4296-4301}-{4296-4301}, ISSN: 0743-1619

    We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value all the oscillators synchronize, resulting in convergence of all phase differences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We also provide a series of bounds for the critical values of the coupling strength.
  • Journal article
    Pecora L, Barahona M, 2005,

    Synchronization of oscillators in complex networks

    , Chaos and Complexity Letters, Vol: 1, Pages: 61-91, ISSN: 1556-3995
  • Conference paper
    Barahona M, Doherty AC, Smaier M, Mahuchi H, Doyle JCet al., 2002,

    Finite horizon model reduction and the appearance of dissipation in Hamiltonian systems

    , Pages: {4563-4568}-{4563-4568}, ISSN: 0191-2216

    An apparent paradox in classical statistical physics is the mechanism by which conservative, time-reversible microscopic dynamics, can give rise to seemingly dissipative behavior. In this paper we use system theoretic tools to show that dissipation can arise as an artifact of incomplete observations over a finite horizon. In addition, this approach allows us to obtain finite-time, low order, approximations of systems with moderate size, and to establish how the approach to the thermodynamic limit depends on the different physical parameters.
  • Journal article
    Barahona M, Pecora LM, 2002,

    Synchronization in small-world systems

    , PHYSICAL REVIEW LETTERS, Vol: 89, ISSN: 0031-9007

    We quantify the dynamical implications of the small-world phenomenon by considering the generic synchronization of oscillator networks of arbitrary topology. The linear stability of the synchronous state is linked to an algebraic condition of the Laplacian matrix of the network. Through numerics and analysis, we show how the addition of random shortcuts translates into improved network synchronizability. Applied to networks of low redundancy, the small-world route produces synchronizability more efficiently than standard deterministic graphs, purely random graphs, and ideal constructive schemes. However, the small-world property does not guarantee synchronizability: the synchronization threshold lies within the boundaries, but linked to the end of the small-world region.
  • Journal article
    Diehl MR, Yaliraki SN, Beckman RA, Barahona M, Heath JRet al., 2002,

    Self-assembled, deterministic carbon nanotube wiring networks

    , ANGEWANDTE CHEMIE-INTERNATIONAL EDITION, Vol: 41, Pages: {353+}-{353+}, ISSN: 1433-7851
  • Journal article
    Poon CS, Barahona M, 2001,

    Titration of chaos with added noise

    , PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, Vol: 98, Pages: {7107-7112}-{7107-7112}, ISSN: 0027-8424

    Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has lad to considerable controversy in many fields. Here we propose a numerical titration procedure as a simple “litmus test” for highly sensitive, specific, and robust detection of chaos in short noisy data without the need for intensive surrogate data testing. We show that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that: (i) faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos; and (ii) gives a relative measure of chaos intensity. Such reliable detection and quantification of chaos under severe conditions of relatively low signal-to-noise ratio is of great interest, as it may open potential practical ways of identifying, forecasting, and controlling complex behaviors in a wide variety of physical, biomedical, and socioeconomic systems.
  • Journal article
    Barahona M, Poon CS, 1996,

    Detection of nonlinear dynamics in short, noisy time series

    , NATURE, Vol: 381, Pages: 215-217, ISSN: 0028-0836

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