1,088 research outputs found
Langevin approach to synchronization of hyperchaotic time-delay dynamics
In this paper, we characterize the synchronization phenomenon of hyperchaotic
scalar non-linear delay dynamics in a fully-developed chaos regime. Our results
rely on the observation that, in that regime, the stationary statistical
properties of a class of hyperchaotic attractors can be reproduced with a
linear Langevin equation, defined by replacing the non-linear delay force by a
delta-correlated noise. Therefore, the synchronization phenomenon can be
analytically characterized by a set of coupled Langevin equations. We apply
this formalism to study anticipated synchronization dynamics subject to
external noise fluctuations as well as for characterizing the effects of
parameter mismatch in a hyperchaotic communication scheme. The same procedure
is applied to second order differential delay equations associated to
synchronization in electro-optical devices. In all cases, the departure with
respect to perfect synchronization is measured through a similarity function.
Numerical simulations in discrete maps associated to the hyperchaotic dynamics
support the formalism.Comment: 12 pages, 6 figure
Phase synchronization in time-delay systems
Though the notion of phase synchronization has been well studied in chaotic
dynamical systems without delay, it has not been realized yet in chaotic
time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In
this article we report the first identification of phase synchronization in
coupled time-delay systems exhibiting hyperchaotic attractor. We show that
there is a transition from non-synchronized behavior to phase and then to
generalized synchronization as a function of coupling strength. These
transitions are characterized by recurrence quantification analysis, by phase
differences based on a new transformation of the attractors and also by the
changes in the Lyapunov exponents. We have found these transitions in coupled
piece-wise linear and in Mackey-Glass time-delay systems.Comment: 4 pages, 3 Figures (To appear in Physical Review E Rapid
Communication
Partially integrable dynamics of hierarchical populations of coupled oscillators
We consider oscillator ensembles consisting of subpopulations of identical
units, with a general heterogeneous coupling between subpopulations. Using the
Watanabe-Strogatz ansatz we reduce the dynamics of the ensemble to a relatively
small number of dynamical variables plus constants of motion. This reduction is
independent of the sizes of subpopulations and remains valid in the
thermodynamic limits. The theory is applied to the standard Kuramoto model and
to the description of two interacting subpopulations, where we report a novel,
quasiperiodic chimera state.Comment: 4 pages, 1 figur
Self-Emerging and Turbulent Chimeras in Oscillator Chains
We report on a self-emerging chimera state in a homogeneous chain of
nonlocally and nonlinearly coupled oscillators. This chimera, i.e. a state with
coexisting regions of complete and partial synchrony, emerges via a
supercritical bifurcation from a homogeneous state and thus does not require
preparation of special initial conditions. We develop a theory of chimera
basing on the equations for the local complex order parameter in the
Ott-Antonsen approximation. Applying a numerical linear stability analysis, we
also describe the instability of the chimera and transition to a phase
turbulence with persistent patches of synchrony
Radiative damping and synchronization in a graphene-based terahertz emitter
We investigate the collective electron dynamics in a recently proposed
graphene-based terahertz emitter under the influence of the radiative damping
effect, which is included self-consistently in a molecular dynamics approach.
We show that under appropriate conditions synchronization of the dynamics of
single electrons takes place, leading to a rise of the oscillating component of
the charge current. The synchronization time depends dramatically on the
applied dc electric field and electron scattering rate, and is roughly
inversely proportional to the radiative damping rate that is determined by the
carrier concentration and the geometrical parameters of the device. The
emission spectra in the synchronized state, determined by the oscillating
current component, are analyzed. The effective generation of higher harmonics
for large values of the radiative damping strength is demonstrated.Comment: 9 pages, 7 figure
Phase resetting of collective rhythm in ensembles of oscillators
Phase resetting curves characterize the way a system with a collective
periodic behavior responds to perturbations. We consider globally coupled
ensembles of Sakaguchi-Kuramoto oscillators, and use the Ott-Antonsen theory of
ensemble evolution to derive the analytical phase resetting equations. We show
the final phase reset value to be composed of two parts: an immediate phase
reset directly caused by the perturbation, and the dynamical phase reset
resulting from the relaxation of the perturbed system back to its dynamical
equilibrium. Analytical, semi-analytical and numerical approximations of the
final phase resetting curve are constructed. We support our findings with
extensive numerical evidence involving identical and non-identical oscillators.
The validity of our theory is discussed in the context of large ensembles
approximating the thermodynamic limit.Comment: submitted to Phys. Rev.
Dynamics of multi-frequency oscillator ensembles with resonant coupling
We study dynamics of populations of resonantly coupled oscillators having
different frequencies. Starting from the coupled van der Pol equations we
derive the Kuramoto-type phase model for the situation, where the natural
frequencies of two interacting subpopulations are in relation 2:1. Depending on
the parameter of coupling, ensembles can demonstrate fully synchronous
clusters, partial synchrony (only one subpopulation synchronizes), or
asynchrony in both subpopulations. Theoretical description of the dynamics
based on the Watanabe-Strogatz approach is developed.Comment: 12 page
Universal Scaling Properties in Large Assemblies of Simple Dynamical Units Driven by Long-Wave Random Forcing
Large assemblies of nonlinear dynamical units driven by a long-wave
fluctuating external field are found to generate strong turbulence with scaling
properties. This type of turbulence is so robust that it persists over a finite
parameter range with parameter-dependent exponents of singularity, and is
insensitive to the specific nature of the dynamical units involved. Whether or
not the units are coupled with their neighborhood is also unimportant. It is
discovered numerically that the derivative of the field exhibits strong spatial
intermittency with multifractal structure.Comment: 10 pages, 7 figures, submitted to PR
Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators
A new behavior type of unidirectionally coupled chaotic oscillators near the
generalized synchronization transition has been detected. It has been shown
that the generalized synchronization appearance is preceded by the intermitted
behavior: close to threshold parameter value the coupled chaotic systems
demonstrate the generalized synchronization most of the time, but there are
time intervals during which the synchronized oscillations are interrupted by
non-synchronous bursts. This type of the system behavior has been called
intermitted generalized synchronization (IGS) by analogy with intermitted lag
synchronization (ILS) [Phys. Rev. E \textbf{62}, 7497 (2000)].Comment: 8 pages, 5 figures, using epl.cls; published in Europhysics Letters.
70, 2 (2005) 169-17
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