809 research outputs found
Effect of noise on coupled chaotic systems
Effect of noise in inducing order on various chaotically evolving systems is
reviewed, with special emphasis on systems consisting of coupled chaotic
elements. In many situations it is observed that the uncoupled elements when
driven by identical noise, show synchronization phenomena where chaotic
trajectories exponentially converge towards a single noisy trajectory,
independent of the initial conditions. In a random neural network, with
infinite range coupling, chaos is suppressed due to noise and the system
evolves towards a fixed point. Spatiotemporal stochastic resonance phenomenon
has been observed in a square array of coupled threshold devices where a
temporal characteristic of the system resonates at a given noise strength. In a
chaotically evolving coupled map lattice with logistic map as local dynamics
and driven by identical noise at each site, we report that the number of
structures (a structure is a group of neighbouring lattice sites for whom
values of the variable follow certain predefined pattern) follow a power-law
decay with the length of the structure. An interesting phenomenon, which we
call stochastic coherence, is also reported in which the abundance and
lifetimes of these structures show characteristic peaks at some intermediate
noise strength.Comment: 21 page LaTeX file for text, 5 Postscript files for figure
Synchronization of spatiotemporal semiconductor lasers and its application in color image encryption
Optical chaos is a topic of current research characterized by
high-dimensional nonlinearity which is attributed to the delay-induced
dynamics, high bandwidth and easy modular implementation of optical feedback.
In light of these facts, which adds enough confusion and diffusion properties
for secure communications, we explore the synchronization phenomena in
spatiotemporal semiconductor laser systems. The novel system is used in a
two-phase colored image encryption process. The high-dimensional chaotic
attractor generated by the system produces a completely randomized chaotic time
series, which is ideal in the secure encoding of messages. The scheme thus
illustrated is a two-phase encryption method, which provides sufficiently high
confusion and diffusion properties of chaotic cryptosystem employed with unique
data sets of processed chaotic sequences. In this novel method of cryptography,
the chaotic phase masks are represented as images using the chaotic sequences
as the elements of the image. The scheme drastically permutes the positions of
the picture elements. The next additional layer of security further alters the
statistical information of the original image to a great extent along the
three-color planes. The intermediate results during encryption demonstrate the
infeasibility for an unauthorized user to decipher the cipher image. Exhaustive
statistical tests conducted validate that the scheme is robust against noise
and resistant to common attacks due to the double shield of encryption and the
infinite dimensionality of the relevant system of partial differential
equations.Comment: 20 pages, 11 figures; Article in press, Optics Communications (2011
Neuronal synchrony: peculiarity and generality
Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their “dynamical repertoire” includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neuronal networks with plastic synapses (synchronization with activity dependent coupling), (ii) synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks (partial synchronization of small composite structures), and (iv) coarse grained synchronization in larger systems (synchronization on a mesoscopic scale
Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors
We, herein, present a new model based on the framework of synchronization to
describe a thermoacoustic system and capture the multiple bifurcations that
such a system undergoes. Instead of applying flame describing function to
depict the unsteady heat release rate as the flame's response to acoustic
perturbation, the new model considers the acoustic field and the unsteady heat
release rate as a pair of nonlinearly coupled damped oscillators. By varying
the coupling strength, multiple dynamical behaviors, including limit cycle
oscillation, quasi-periodic oscillation, strange nonchaos, and chaos can be
captured. Furthermore, the model was able to qualitatively replicate the
different behaviors of a laminar thermoacoustic system observed in experiments
by Kabiraj et al.~[Chaos 22, 023129 (2012)]. By analyzing the temporal
variation of the phase difference between heat release rate oscillations and
pressure oscillations under different dynamical states, we show that the
characteristics of the dynamical states depend on the nature of synchronization
between the two signals, which is consistent with previous experimental
findings.Comment: 18 pages, 7 figure
Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators
In this set of lectures, we review briefly some of the recent developments in
the study of the chaotic dynamics of nonlinear oscillators, particularly of
damped and driven type. By taking a representative set of examples such as the
Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain
the various bifurcations and chaos phenomena associated with these systems. We
use numerical and analytical as well as analogue simulation methods to study
these systems. Then we point out how controlling of chaotic motions can be
effected by algorithmic procedures requiring minimal perturbations. Finally we
briefly discuss how synchronization of identically evolving chaotic systems can
be achieved and how they can be used in secure communications.Comment: 31 pages (24 figures) LaTeX. To appear Springer Lecture Notes in
Physics Please Lakshmanan for figures (e-mail: [email protected]
Effect of fiber dispersion on broadband chaos communications implemented by electro-optic nonlinear delay phase dynamics
We investigate theoretically and experimentally
the detrimental e ect of ber dispersion on the synchroniza-
tion of an optoelectronic phase chaos cryptosystem. We
evaluate the root-mean square synchronization error and
the cancellation spectra between the emitter and the re-
ceiver in order to characterize the quality of the optical
ber communication link. These two indicators explicitly
show in temporal and spectral domain how ber dispersion
does negatively a ect the phase chaos cancellation at the re-
ceiver stage. We demonstrate that the dispersion manage-
ment techniques used in conventional optical ber networks,
such as dispersion-compensating modules/ bers or disper-
sion shifted bers, are also e cient to strongly reduce the
detrimental e ects of ber propagation in phase chaos com-
munications. This compatibility therefore opens the way to
a successful integration of more than 10-Gb/s phase chaos
communications systems in existing networks, even when
the ber link spans over more than 100 km.Peer reviewe
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