4,169 research outputs found
From Kardar-Parisi-Zhang scaling to explosive desynchronization in arrays of limit-cycle oscillators
We study the synchronization physics of 1D and 2D oscillator lattices subject
to noise and predict a dynamical transition that leads to a sudden drastic
increase of phase diffusion. Our analysis is based on the widely applicable
Kuramoto-Sakaguchi model, with local couplings between oscillators. For smooth
phase fields, the time evolution can initially be described by a surface growth
model, the Kardar-Parisi-Zhang (KPZ) theory. We delineate the regime in which
one can indeed observe the universal KPZ scaling in 1D lattices. For larger
couplings, both in 1D and 2D, we observe a stochastic dynamical instability
that is linked to an apparent finite-time singularity in a related KPZ lattice
model. This has direct consequences for the frequency stability of coupled
oscillator lattices, and it precludes the observation of non-Gaussian
KPZ-scaling in 2D lattices.Comment: 9 pages, 5 figure
Phaselocked patterns and amplitude death in a ring of delay coupled limit cycle oscillators
We study the existence and stability of phaselocked patterns and amplitude
death states in a closed chain of delay coupled identical limit cycle
oscillators that are near a supercritical Hopf bifurcation. The coupling is
limited to nearest neighbors and is linear. We analyze a model set of discrete
dynamical equations using the method of plane waves. The resultant dispersion
relation, which is valid for any arbitrary number of oscillators, displays
important differences from similar relations obtained from continuum models. We
discuss the general characteristics of the equilibrium states including their
dependencies on various system parameters. We next carry out a detailed linear
stability investigation of these states in order to delineate their actual
existence regions and to determine their parametric dependence on time delay.
Time delay is found to expand the range of possible phaselocked patterns and to
contribute favorably toward their stability. The amplitude death state is
studied in the parameter space of time delay and coupling strength. It is shown
that death island regions can exist for any number of oscillators N in the
presence of finite time delay. A particularly interesting result is that the
size of an island is independent of N when N is even but is a decreasing
function of N when N is odd.Comment: 23 pages, 12 figures (3 of the figures in PNG format, separately from
TeX); minor additions; typos correcte
Emergence of multicluster chimera states
We thank Prof. L. Huang for helpful discussions. This work was partially supported by ARO under Grant No. W911NF-14-1-0504 and by NSF of China under Grant No. 11275003. The visit of NY to Arizona State University was partially sponsored by Prof. Z. Zheng and the State Scholarship Fund of China.Peer reviewedPublisher PD
Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
A chimera state is a spatio-temporal pattern in a network of identical
coupled oscillators in which synchronous and asynchronous oscillation coexist.
This state of broken symmetry, which usually coexists with a stable spatially
symmetric state, has intrigued the nonlinear dynamics community since its
discovery in the early 2000s. Recent experiments have led to increasing
interest in the origin and dynamics of these states. Here we review the history
of research on chimera states and highlight major advances in understanding
their behaviour.Comment: 26 pages, 3 figure
Birhythmicity, Synchronization, and Turbulence in an Oscillatory System with Nonlocal Inertial Coupling
We consider a model where a population of diffusively coupled limit-cycle
oscillators, described by the complex Ginzburg-Landau equation, interacts
nonlocally via an inertial field. For sufficiently high intensity of nonlocal
inertial coupling, the system exhibits birhythmicity with two oscillation modes
at largely different frequencies. Stability of uniform oscillations in the
birhythmic region is analyzed by means of the phase dynamics approximation.
Numerical simulations show that, depending on its parameters, the system has
irregular intermittent regimes with local bursts of synchronization or
desynchronization.Comment: 21 pages, many figures. Paper accepted on Physica
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