35,017 research outputs found
Synchronization with partial state coupling on SO(n)
This paper studies autonomous synchronization of k agents whose states evolve
on SO(n), but which are only coupled through the action of their states on one
"reference vector" in Rn for each link. Thus each link conveys only partial
state information at each time, and to reach synchronization agents must
combine this information over time or throughout the network. A natural
gradient coupling law for synchronization is proposed. Extensive convergence
analysis of the coupled agents is provided, both for fixed and time-varying
reference vectors. The case of SO(3) with fixed reference vectors is discussed
in more detail. For comparison, we also treat the equivalent setting in Rn,
i.e. with states in Rn and connected agents comparing scalar product of their
states with a reference vector.Comment: to be submitted to SIAM Journal on Control and Optimizatio
Analysis of Nonlinear Synchronization Dynamics of Oscillator Networks by Laplacian Spectral Methods
We analyze the synchronization dynamics of phase oscillators far from the
synchronization manifold, including the onset of synchronization on scale-free
networks with low and high clustering coefficients. We use normal coordinates
and corresponding time-averaged velocities derived from the Laplacian matrix,
which reflects the network's topology. In terms of these coordinates,
synchronization manifests itself as a contraction of the dynamics onto
progressively lower-dimensional submanifolds of phase space spanned by
Laplacian eigenvectors with lower eigenvalues. Differences between high and low
clustering networks can be correlated with features of the Laplacian spectrum.
For example, the inhibition of full synchoronization at high clustering is
associated with a group of low-lying modes that fail to lock even at strong
coupling, while the advanced partial synchronizationat low coupling noted
elsewhere is associated with high-eigenvalue modes.Comment: Revised version: References added, introduction rewritten, additional
minor changes for clarit
Synchronization Transition of Identical Phase Oscillators in a Directed Small-World Network
We numerically study a directed small-world network consisting of
attractively coupled, identical phase oscillators. While complete
synchronization is always stable, it is not always reachable from random
initial conditions. Depending on the shortcut density and on the asymmetry of
the phase coupling function, there exists a regime of persistent chaotic
dynamics. By increasing the density of shortcuts or decreasing the asymmetry of
the phase coupling function, we observe a discontinuous transition in the
ability of the system to synchronize. Using a control technique, we identify
the bifurcation scenario of the order parameter. We also discuss the relation
between dynamics and topology and remark on the similarity of the
synchronization transition to directed percolation.Comment: This article has been accepted in AIP, Chaos. After it is published,
it will be found at http://chaos.aip.org/, 12 pages, 9 figures, 1 tabl
Generalized Chaotic Synchronizationin Coupled Ginzburg-Landau Equations
Generalized synchronization is analyzed in unidirectionally coupled
oscillatory systems exhibiting spatiotemporal chaotic behavior described by
Ginzburg-Landau equations. Several types of coupling betweenthe systems are
analyzed. The largest spatial Lyapunov exponent is proposed as a new
characteristic of the state of a distributed system, and its calculation is
described for a distributed oscillatory system. Partial generalized
synchronization is introduced as a new type of chaotic synchronization in
spatially nonuniform distributed systems. The physical mechanisms responsible
for the onset of generalized chaotic synchronization in spatially distributed
oscillatory systems are elucidated. It is shown that the onset of generalized
chaotic synchronization is described by a modified Ginzburg-Landau equation
with additional dissipation irrespective of the type of coupling. The effect of
noise on the onset of a generalized synchronization regime in coupled
distributed systems is analyzed.Comment: 12 page
Emergence of synchronization induced by the interplay between two prisoner's dilemma games with volunteering in small-world networks
We studied synchronization between prisoner's dilemma games with voluntary
participation in two Newman-Watts small-world networks. It was found that there
are three kinds of synchronization: partial phase synchronization, total phase
synchronization and complete synchronization, for varied coupling factors.
Besides, two games can reach complete synchronization for the large enough
coupling factor. We also discussed the effect of coupling factor on the
amplitude of oscillation of density.Comment: 6 pages, 4 figure
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