1,842 research outputs found
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
Global generalized synchronization in networks of different time-delay systems
We show that global generalized synchronization (GS) exists in structurally
different time-delay systems, even with different orders, with quite different
fractal (Kaplan-Yorke) dimensions, which emerges via partial GS in
symmetrically coupled regular networks. We find that there exists a smooth
transformation in such systems, which maps them to a common GS manifold as
corroborated by their maximal transverse Lyapunov exponent. In addition, an
analytical stability condition using the Krasvoskii-Lyapunov theory is deduced.
This phenomenon of GS in strongly distinct systems opens a new way for an
effective control of pathological synchronous activity by means of extremely
small perturbations to appropriate variables in the synchronization manifold.Comment: 6 pages, 4 figures, Accepted for publication in Europhys. Let
Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
Chaos synchronization in a ring of diffusively coupled nonlinear oscillators
driven by an external identical oscillator is studied. Based on numerical
simulations we show that by introducing additional couplings at -th
oscillators in the ring, where is an integer and is the maximum
number of synchronized oscillators in the ring with a single coupling, the
maximum number of oscillators that can be synchronized can be increased
considerably beyond the limit restricted by size instability. We also
demonstrate that there exists an exponential relation between the number of
oscillators that can support stable synchronization in the ring with the
external drive and the critical coupling strength with a scaling
exponent . The critical coupling strength is calculated by numerically
estimating the synchronization error and is also confirmed from the conditional
Lyapunov exponents (CLEs) of the coupled systems. We find that the same scaling
relation exists for couplings between the drive and the ring. Further, we
have examined the robustness of the synchronous states against Gaussian white
noise and found that the synchronization error exhibits a power-law decay as a
function of the noise intensity indicating the existence of both noise-enhanced
and noise-induced synchronizations depending on the value of the coupling
strength . In addition, we have found that shows an
exponential decay as a function of the number of additional couplings. These
results are demonstrated using the paradigmatic models of R\"ossler and Lorenz
oscillators.Comment: Accepted for Publication in Physical Review
Nonlinear Dynamics of Moving Curves and Surfaces: Applications to Physical Systems
The subject of moving curves (and surfaces) in three dimensional space (3-D)
is a fascinating topic not only because it represents typical nonlinear
dynamical systems in classical mechanics, but also finds important applications
in a variety of physical problems in different disciplines. Making use of the
underlying geometry, one can very often relate the associated evolution
equations to many interesting nonlinear evolution equations, including soliton
possessing nonlinear dynamical systems. Typical examples include dynamics of
filament vortices in ordinary and superfluids, spin systems, phases in
classical optics, various systems encountered in physics of soft matter, etc.
Such interrelations between geometric evolution and physical systems have
yielded considerable insight into the underlying dynamics. We present a
succinct tutorial analysis of these developments in this article, and indicate
further directions. We also point out how evolution equations for moving
surfaces are often intimately related to soliton equations in higher
dimensions.Comment: Review article, 38 pages, 7 figs. To appear in Int. Jour. of Bif. and
Chao
Manifestations of Power and Marginality in Marriage Practices: A Qualitative Analysis of Sukuma Songs in Tanzania
This study examined manifestations of power and marginality in Sukuma marriage practices. The study was conducted in Kishapu District, Tanzania. It drew its materials from Sukuma marriage rituals, which include singing and performance of songs. The study adopted an ethnographic research design and used both primary and secondary data to analyse the construction of gender roles in songs and societal views. The songs were observed at live performances, and data related to their composition, interpretation, and impact were gathered through interviews with the singers. Thematic Code Analysis was used to analyze the data, which were then interpreted based on poststructuralist theory. The results obtained showed that Sukuma marriage songs present and propagate imbalanced gender roles. It was further found that these songs impliedly bolster gender inequality leading to women’s subordination and men’s authority over women in Sukuma society
Experimental confirmation of chaotic phase synchronization in coupled time-delayed electronic circuits
We report the first experimental demonstration of chaotic phase
synchronization (CPS) in unidirectionally coupled time-delay systems using
electronic circuits. We have also implemented experimentally an efficient
methodology for characterizing CPS, namely the localized sets. Snapshots of the
evolution of coupled systems and the sets as observed from the oscilloscope
confirming CPS are shown experimentally. Numerical results from different
approaches, namely phase differences, localized sets, changes in the largest
Lyapunov exponents and the correlation of probability of recurrence
(), corroborate the experimental observations.Comment: Physical_Review_E_82_065201(R) 201
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