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Title: Synchronization of mobile chaotic oscillator networks

Abstract

We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, amore » linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.« less

Authors:
 [1];  [2];  [3]
  1. Center for Spatial Information Science, The University of Tokyo, 277-8568 Chiba (Japan)
  2. Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany and Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen (United Kingdom)
  3. Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain and Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona (Spain)
Publication Date:
OSTI Identifier:
22596390
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 26; Journal Issue: 9; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; CHAOS THEORY; LYAPUNOV METHOD; NOISE; OSCILLATORS; SYNCHRONIZATION; TOPOLOGY

Citation Formats

Fujiwara, Naoya, E-mail: fujiwara@csis.u-tokyo.ac.jp, Kurths, Jürgen, and Díaz-Guilera, Albert. Synchronization of mobile chaotic oscillator networks. United States: N. p., 2016. Web. doi:10.1063/1.4962129.
Fujiwara, Naoya, E-mail: fujiwara@csis.u-tokyo.ac.jp, Kurths, Jürgen, & Díaz-Guilera, Albert. Synchronization of mobile chaotic oscillator networks. United States. doi:10.1063/1.4962129.
Fujiwara, Naoya, E-mail: fujiwara@csis.u-tokyo.ac.jp, Kurths, Jürgen, and Díaz-Guilera, Albert. Thu . "Synchronization of mobile chaotic oscillator networks". United States. doi:10.1063/1.4962129.
@article{osti_22596390,
title = {Synchronization of mobile chaotic oscillator networks},
author = {Fujiwara, Naoya, E-mail: fujiwara@csis.u-tokyo.ac.jp and Kurths, Jürgen and Díaz-Guilera, Albert},
abstractNote = {We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.},
doi = {10.1063/1.4962129},
journal = {Chaos (Woodbury, N. Y.)},
number = 9,
volume = 26,
place = {United States},
year = {Thu Sep 15 00:00:00 EDT 2016},
month = {Thu Sep 15 00:00:00 EDT 2016}
}