8,514 research outputs found
Finite-size scaling of synchronized oscillation on complex networks
The onset of synchronization in a system of random frequency oscillators
coupled through a random network is investigated. Using a mean-field
approximation, we characterize sample-to-sample fluctuations for networks of
finite size, and derive the corresponding scaling properties in the critical
region. For scale-free networks with the degree distribution at large , we found that the finite size exponent
takes on the value 5/2 when , the same as in the globally coupled
Kuramoto model. For highly heterogeneous networks (),
and the order parameter exponent depend on . The analytic
expressions for these exponents obtained from the mean field theory are shown
to be in excellent agreement with data from extensive numerical simulations.Comment: 7 page
Entrainment and synchronization in networks of Rayleigh-van der Pol oscillators with diffusive and Haken-Kelso-Bunz couplings
We analyze a network of non-identical Rayleigh–van der Pol (RvdP) oscillators interconnected through either diffusive or nonlinear coupling functions. The work presented here extends existing results on the case of two nonlinearly coupled RvdP oscillators to the problem of considering a network of three or more of them. Specifically, we study synchronization and entrainment in networks of heterogeneous RvdP oscillators and contrast the effects of diffusive linear coupling strategies with the nonlinear Haken–Kelso–Bunz coupling, originally introduced to study human bimanual experiments. We show how convergence of the error among the nodes’ trajectories toward a bounded region is possible with both linear and nonlinear coupling functions. Under the assumption that the network is connected, simple, and undirected, analytical results are obtained to prove boundedness of the error when the oscillators are coupled diffusively. All results are illustrated by way of numerical examples and compared with the experimental findings available in the literature on synchronization of people rocking chairs, confirming the effectiveness of the model we propose to capture some of the features of human group synchronization observed experimentally in the previous literature
Synchronization in networks of diffusively coupled nonlinear systems:robustness against time-delays
In this manuscript, we study the problem of robust synchronization in
networks of diffusively time-delayed coupled nonlinear systems. In particular,
we prove that, under some mild conditions on the input-output dynamics of the
systems and the network topology, there always exists a unimodal region in the
parameter space (coupling strength versus time-delay), such that if they belong
to this region, the systems synchronize. Moreover, we show how this unimodal
region scales with the network topology, which, in turn, provides useful
insights on how to design the network topology to maximize robustness against
time-delays. The results are illustrated by extensive simulation experiments of
time-delayed coupled Hindmarsh-Rose neural chaotic oscillators
Breathing synchronization in interconnected networks
Global synchronization in a complex network of oscillators emerges from the
interplay between its topology and the dynamics of the pairwise interactions
among its numerous components. When oscillators are spatially separated,
however, a time delay appears in the interaction which might obstruct
synchronization. Here we study the synchronization properties of interconnected
networks of oscillators with a time delay between networks and analyze the
dynamics as a function of the couplings and communication lag. We discover a
new breathing synchronization regime, where two groups appear in each network
synchronized at different frequencies. Each group has a counterpart in the
opposite network, one group is in phase and the other in anti-phase with their
counterpart. For strong couplings, instead, networks are internally
synchronized but a phase shift between them might occur. The implications of
our findings on several socio-technical and biological systems are discussed.Comment: 7 pages, 3 figures + 3 pages of Supplemental Materia
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