520 research outputs found
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]
Chaos-based communication scheme using proportional and proportional-integral observers
In this paper, we propose a new chaos-based communication scheme using the observers. The novelty lies in the masking procedure that is employed to hide the confidential information using the chaotic oscillator. We use a combination of the addition and inclusion methods to mask the information. The performance of two observers, the proportional observer (P-observer) and the proportional integral observer (PI-observer) is compared that are employed as receivers for the proposed communication scheme. We show that the P-observer is not suitable scheme since it imposes unpractical constraints on the messages to be transmitted. On the other hand, we show that the PI-observer is the better solution because it allows greater flexibility in choosing the gains of the observer and does not impose any unpractical restrictions on the message
Quantum internet using code division multiple access
A crucial open problem in large-scale quantum networks is how to efficiently
transmit quantum data among many pairs of users via a common data-transmission
medium. We propose a solution by developing a quantum code division multiple
access (q-CDMA) approach in which quantum information is chaotically encoded to
spread its spectral content, and then decoded via chaos synchronization to
separate different sender-receiver pairs. In comparison to other existing
approaches, such as frequency division multiple access (FDMA), the proposed
q-CDMA can greatly increase the information rates per channel used, especially
for very noisy quantum channels.Comment: 29 pages, 6 figure
Bifurcation structure of two Coupled Periodically driven double-well Duffing Oscillators
The bifurcation structure of coupled periodically driven double-well Duffing
oscillators is investigated as a function of the strength of the driving force
and its frequency . We first examine the stability of the steady
state in linear response, and classify the different types of bifurcation
likely to occur in this model. We then explore the complex behaviour associated
with these bifurcations numerically. Our results show many striking departures
from the behaviour of coupled driven Duffing Oscillators with single
well-potentials, as characterised by Kozlowski et al \cite{k1}. In addition to
the well known routes to chaos already encountered in a one-dimensional Duffing
oscillator, our model exhibits imbricated period-doubling of both types,
symmetry-breaking, sudden chaos and a great abundance of Hopf bifurcations,
many of which occur more than once for a given driving frequency. We explore
the chaotic behaviour of our model using two indicators, namely Lyapunov
exponents and the power spectrum. Poincar\'e cross-sections and phase portraits
are also plotted to show the manifestation of coexisting periodic and chaotic
attractors including the destruction of tori doubling.Comment: 16 pages, 8 figure
Basin stability approach for quantifying responses of multistable systems with parameters mismatch
Acknowledgement This work is funded by the National Science Center Poland based on the decision number DEC-2015/16/T/ST8/00516. PB is supported by the Foundation for Polish Science (FNP).Peer reviewedPublisher PD
Hidden attractors in fundamental problems and engineering models
Recently a concept of self-excited and hidden attractors was suggested: an
attractor is called a self-excited attractor if its basin of attraction
overlaps with neighborhood of an equilibrium, otherwise it is called a hidden
attractor. For example, hidden attractors are attractors in systems with no
equilibria or with only one stable equilibrium (a special case of
multistability and coexistence of attractors). While coexisting self-excited
attractors can be found using the standard computational procedure, there is no
standard way of predicting the existence or coexistence of hidden attractors in
a system. In this plenary survey lecture the concept of self-excited and hidden
attractors is discussed, and various corresponding examples of self-excited and
hidden attractors are considered
Chaos of the Relativistic Parametrically Forced van der Pol Oscillator
A manifestly relativistically covariant form of the van der Pol oscillator in
1+1 dimensions is studied. We show that the driven relativistic equations, for
which and are coupled, relax very quickly to a pair of identical
decoupled equations, due to a rapid vanishing of the ``angular momentum'' (the
boost in 1+1 dimensions). A similar effect occurs in the damped driven
covariant Duffing oscillator previously treated. This effect is an example of
entrainment, or synchronization (phase locking), of coupled chaotic systems.
The Lyapunov exponents are calculated using the very efficient method of Habib
and Ryne. We show a Poincar\'e map that demonstrates this effect and maintains
remarkable stability in spite of the inevitable accumulation of computer error
in the chaotic region. For our choice of parameters, the positive Lyapunov
exponent is about 0.242 almost independently of the integration method.Comment: 8 Latex pages including 12 figures. To be published in Phys. Lett.
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