TY - JOUR

T1 - Synchronization of mobile chaotic oscillator networks

AU - Fujiwara, Naoya

AU - Kurths, Jürgen

AU - Díaz-Guilera, Albert

N1 - Funding Information:
N.F. was supported by the Aihara Project, the FIRST program from JSPS, initiated by CSTP, and JSPS KAKENHI Grant No. 15K16061. A.D.-G. acknowledges the support from Generalitat de Catalunya (2014SGR608) and Spanish MICINN (PR2008-0114, FIS2012-38266, and FIS2015-71582). J.K. and N.F. are supported by FET Open project SUMO (Grant Agreement No. 266722).

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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.

AB - 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.

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U2 - 10.1063/1.4962129

DO - 10.1063/1.4962129

M3 - Article

AN - SCOPUS:84986563445

VL - 26

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 9

M1 - 094824

ER -