1,913 research outputs found
Two-oscillator model of trapped-modes interaction in a nonlinear bilayer fish-scale metamaterial
We discuss the similarity between the nature of resonant oscillations in two
nonlinear systems, namely, a chain of coupled Duffing oscillators and a bilayer
fish-scale metamaterial. In such systems two different resonant states arise
which differ in their spectral lines. The spectral line of the first resonant
state has a Lorentzian form, while the second one has a Fano form. This
difference leads to a specific nonlinear response of the systems which
manifests itself in appearance of closed loops in spectral lines and bending
and overlapping of resonant curves. Conditions of achieving bistability and
multistability are found out.Comment: 14 pages, 6 figure
The Kuramoto model: A simple paradigm for synchronization phenomena
Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included
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
Asymptotic description of transients and synchronized states of globally coupled oscillators
A two-time scale asymptotic method has been introduced to analyze the
multimodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in
the high-frequency limit. The method allows to uncouple the probability density
in different components corresponding to the different peaks of the oscillator
frequency distribution. Each component evolves toward a stationary state in a
comoving frame and the overall order parameter can be reconstructed by
combining them. Synchronized phases are a combination of traveling waves and
incoherent solutions depending on parameter values. Our results agree very well
with direct numerical simulations of the nonlinear Fokker-Planck equation for
the probability density. Numerical results have been obtained by finite
differences and a spectral method in the particular case of bimodal (symmetric
and asymmetric) frequency distribution with or without external field. We also
recover in a very easy and intuitive way the only other known analytical
results: those corresponding to reflection-symmetric bimodal frequency
distributions near bifurcation points.Comment: Revtex,12 pag.,9 fig.;submitted to Physica
Coexisting synchronous and asynchronous states in locally coupled array of oscillators by partial self-feedback control
We report the emergence of coexisting synchronous and asynchronous
subpopulations of oscillators in one dimensional arrays of identical
oscillators by applying a self-feedback control. When a self-feedback is
applied to a subpopulation of the array, similar to chimera states, it splits
into two/more sub-subpopulations coexisting in coherent and incoherent states
for a range of self-feedback strength. By tuning the coupling between the
nearest neighbors and the amount of self-feedback in the perturbed
subpopulation, the size of the coherent and the incoherent sub-subpopulations
in the array can be controlled, although the exact size of them is
unpredictable. We present numerical evidence using the Landau-Stuart (LS)
system and the Kuramoto-Sakaguchi (KS) phase model.Comment: 13 pages, 13 figures, accepted for publication in CHAOS (July 2017
Time Delay Effects on Coupled Limit Cycle Oscillators at Hopf Bifurcation
We present a detailed study of the effect of time delay on the collective
dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple
model consisting of just two oscillators with a time delayed coupling, the
bifurcation diagram obtained by numerical and analytical solutions shows
significant changes in the stability boundaries of the amplitude death, phase
locked and incoherent regions. A novel result is the occurrence of amplitude
death even in the absence of a frequency mismatch between the two oscillators.
Similar results are obtained for an array of N oscillators with a delayed mean
field coupling and the regions of such amplitude death in the parameter space
of the coupling strength and time delay are quantified. Some general analytic
results for the N tending to infinity (thermodynamic) limit are also obtained
and the implications of the time delay effects for physical applications are
discussed.Comment: 20 aps formatted revtex pages (including 13 PS figures); Minor
changes over the previous version; To be published in Physica
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