3,354 research outputs found
Lag synchronization and scaling of chaotic attractor in coupled system
We report a design of delay coupling for lag synchronization in two
unidirectionally coupled chaotic oscillators. A delay term is introduced in the
definition of the coupling to target any desired lag between the driver and the
response. The stability of the lag synchronization is ensured by using the
Hurwitz matrix stability. We are able to scale up or down the size of a driver
attractor at a response system in presence of a lag. This allows compensating
the attenuation of the amplitude of a signal during transmission through a
delay line. The delay coupling is illustrated with numerical examples of 3D
systems, the Hindmarsh-Rose neuron model, the R\"ossler system and a Sprott
system and, a 4D system. We implemented the coupling in electronic circuit to
realize any desired lag synchronization in chaotic oscillators and scaling of
attractors.Comment: 10 pages, 7 figure
Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks
We study projective-anticipating, projective, and projective-lag
synchronization of time-delayed chaotic systems on random networks. We relax
some limitations of previous work, where projective-anticipating and
projective-lag synchronization can be achieved only on two coupled chaotic
systems. In this paper, we can realize projective-anticipating and
projective-lag synchronization on complex dynamical networks composed by a
large number of interconnected components. At the same time, although previous
work studied projective synchronization on complex dynamical networks, the
dynamics of the nodes are coupled partially linear chaotic systems. In this
paper, the dynamics of the nodes of the complex networks are time-delayed
chaotic systems without the limitation of the partial-linearity. Based on the
Lyapunov stability theory, we suggest a generic method to achieve the
projective-anticipating, projective, and projective-lag synchronization of
time-delayed chaotic systems on random dynamical networks and find both the
existence and sufficient stability conditions. The validity of the proposed
method is demonstrated and verified by examining specific examples using Ikeda
and Mackey-Glass systems on Erdos-Renyi networks.Comment: 14 pages, 6 figure
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
Estimation of communication-delays through adaptive synchronization of chaos
This paper deals with adaptive synchronization of chaos in the presence of
time-varying communication-delays. We consider two bidirectionally coupled
systems that seek to synchronize through a signal that each system sends to the
other one and is transmitted with an unknown time-varying delay. We show that
an appropriate adaptive strategy can be devised that is successful in
dynamically identifying the time-varying delay and in synchronizing the two
systems. The performance of our strategy with respect to the choice of the
initial conditions and the presence of noise in the communication channels is
tested by using numerical simulations. Another advantage of our approach is
that in addition to estimating the communication-delay, the adaptive strategy
could be used to simultaneously identify other parameters, such as e.g., the
unknown time-varying amplitude of the received signal.Comment: Accepted for publication in Chaos, Solitons & Fractal
Synchronization of chaotic networks with time-delayed couplings: An analytic study
Networks of nonlinear units with time-delayed couplings can synchronize to a
common chaotic trajectory. Although the delay time may be very large, the units
can synchronize completely without time shift. For networks of coupled
Bernoulli maps, analytic results are derived for the stability of the chaotic
synchronization manifold. For a single delay time, chaos synchronization is
related to the spectral gap of the coupling matrix. For networks with multiple
delay times, analytic results are obtained from the theory of polynomials.
Finally, the analytic results are compared with networks of iterated tent maps
and Lang-Kobayashi equations which imitate the behaviour of networks of
semiconductor lasers
Parameter mismatches,variable delay times and synchronization in time-delayed systems
We investigate synchronization between two unidirectionally linearly coupled
chaotic non-identical time-delayed systems and show that parameter mismatches
are of crucial importance to achieve synchronization. We establish that
independent of the relation between the delay time in the coupled systems and
the coupling delay time, only retarded synchronization with the coupling delay
time is obtained. We show that with parameter mismatch or without it neither
complete nor anticipating synchronization occurs. We derive existence and
stability conditions for the retarded synchronization manifold. We demonstrate
our approach using examples of the Ikeda and Mackey-Glass models. Also for the
first time we investigate chaos synchronization in time-delayed systems with
variable delay time and find both existence and sufficient stability conditions
for the retarded synchronization manifold with the coupling delay lag time.
Also for the first time we consider synchronization between two
unidirectionally coupled chaotic multi-feedback Ikeda systems and derive
existence and stability conditions for the different anticipating, lag, and
complete synchronization regimes.Comment: 12 page
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
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