1,276 research outputs found
Existence of anticipatory, complete and lag synchronizations in time-delay systems
Existence of different kinds of synchronizations, namely anticipatory,
complete and lag type synchronizations (both exact and approximate), are shown
to be possible in time-delay coupled piecewise linear systems. We deduce
stability condition for synchronization of such unidirectionally coupled
systems following Krasovskii-Lyapunov theory. Transition from anticipatory to
lag synchronization via complete synchronization as a function of coupling
delay is discussed. The existence of exact synchronization is preceded by a
region of approximate synchronization from desynchronized state as a function
of a system parameter, whose value determines the stability condition for
synchronization. The results are corroborated by the nature of similarity
functions. A new type of oscillating synchronization that oscillates between
anticipatory, complete and lag synchronization, is identified as a consequence
of delay time modulation with suitable stability condition.Comment: 5 Figures 9 page
Delay time modulation induced oscillating synchronization and intermittent anticipatory/lag and complete synchronizations in time-delay nonlinear dynamical systems
Existence of a new type of oscillating synchronization that oscillates
between three different types of synchronizations (anticipatory, complete and
lag synchronizations) is identified in unidirectionally coupled nonlinear
time-delay systems having two different time-delays, that is feedback delay
with a periodic delay time modulation and a constant coupling delay.
Intermittent anticipatory, intermittent lag and complete synchronizations are
shown to exist in the same system with identical delay time modulations in both
the delays. The transition from anticipatory to complete synchronization and
from complete to lag synchronization as a function of coupling delay with
suitable stability condition is discussed. The intermittent anticipatory and
lag synchronizations are characterized by the minimum of similarity functions
and the intermittent behavior is characterized by a universal asymptotic
power law distribution. It is also shown that the delay time carved
out of the trajectories of the time-delay system with periodic delay time
modulation cannot be estimated using conventional methods, thereby reducing the
possibility of decoding the message by phase space reconstruction.Comment: accepted for publication in CHAOS, revised in response to referees
comment
Phase Synchronization in Unidirectionally Coupled Ikeda Time-delay Systems
Phase synchronization in unidirectionally coupled Ikeda time-delay systems
exhibiting non-phase-coherent hyperchaotic attractors of complex topology with
highly interwoven trajectories is studied. It is shown that in this set of
coupled systems phase synchronization (PS) does exist in a range of the
coupling strength which is preceded by a transition regime (approximate PS) and
a nonsynchronous regime. However, exact generalized synchronization does not
seem to occur in the coupled Ikeda systems (for the range of parameters we have
studied) even for large coupling strength, in contrast to our earlier studies
in coupled piecewise-linear and Mackey-Glass systems
\cite{dvskml2006,dvskml2008}. The above transitions are characterized in terms
of recurrence based indices, namely generalized autocorrelation function
, correlation of probability of recurrence (CPR), joint probability of
recurrence (JPR) and similarity of probability of recurrence (SPR). The
existence of phase synchronization is also further confirmed by typical
transitions in the Lyapunov exponents of the coupled Ikeda time-delay systems
and also using the concept of localized sets.Comment: 10 pages, 7 figure
Generalizing the transition from amplitude to oscillation death in coupled oscillators
Peer reviewedPublisher PD
Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems
The existence of anticipatory, complete and lag synchronization in a single
system having two different time-delays, that is feedback delay and
coupling delay , is identified. The transition from anticipatory to
complete synchronization and from complete to lag synchronization as a function
of coupling delay with suitable stability condition is discussed. The
existence of anticipatory and lag synchronization is characterized both by the
minimum of similarity function and the transition from on-off intermittency to
periodic structure in laminar phase distribution.Comment: 14 Pages and 12 Figure
Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force
We identify a novel route to the birth of a strange nonchaotic attractor
(SNA) in a quasiperiodically forced electronic circuit with a nonsinusoidal
(square wave) force as one of the quasiperiodic forces through numerical and
experimental studies. We find that bubbles appear in the strands of the
quasiperiodic attractor due to the instability induced by the additional square
wave type force. The bubbles then enlarge and get increasingly wrinkled as a
function of the control parameter. Finally, the bubbles get extremely wrinkled
(while the remaining parts of the strands of the torus remain largely
unaffected) resulting in the birth of the SNA which we term as the
\emph{bubbling route to SNA}. We characterize and confirm this birth from both
experimental and numerical data by maximal Lyapunov exponents and their
variance, Poincar\'e maps, Fourier amplitude spectra and spectral distribution
function. We also strongly confirm the birth of SNA via the bubbling route by
the distribution of the finite-time Lyapunov exponents.Comment: 11 pages. 11 figures, Accepted for publication in Phys. Rev.
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