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    Dynamical network size estimation from local observations
    ([London] : IOP, 2020) Tang, Xiuchuan; Huo, Wei; Yuan, Ye; Li, Xiuting; Shi, Ling; Kurths, Jürgen
    Here we present a method to estimate the total number of nodes of a network using locally observed response dynamics. The algorithm has the following advantages: (a) it is data-driven. Therefore it does not require any prior knowledge about the model; (b) it does not need to collect measurements from multiple stimulus; and (c) it is distributed as it uses local information only, without any prior information about the global network. Even if only a single node is measured, the exact network size can be correctly estimated using a single trajectory. The proposed algorithm has been applied to both linear and nonlinear networks in simulation, illustrating the applicability to real-world physical networks. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.
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    Attractors for semilinear equations of viscoelasticity with very low disspation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Gatti, Stefania; Miranville, Alain; Pata, Vittorino; Zelik, Sergey
    We analyze a differential system arising in the theory of isothermal viscoelasticity. This system is equivalent to an integrodifferential equation of hyperbolic type with a cubic nonlinearity, where the dissipation mechanism is contained only in the convolution integral, accounting for the past history of the displacement. In particular, we consider here a convolution kernel which entails an extremely weak dissipation. In spite of that, we show that the related dynamical system possesses a global attractor of optimal regularity.