1,727 research outputs found
Secure Communication using Compound Signal from Generalized Synchronizable Chaotic Systems
By considering generalized synchronizable chaotic systems, the
drive-auxiliary system variables are combined suitably using encryption key
functions to obtain a compound chaotic signal. An appropriate feedback loop is
constructed in the response-auxiliary system to achieve synchronization among
the variables of the drive-auxiliary and response-auxiliary systems. We apply
this approach to transmit analog and digital information signals in which the
quality of the recovered signal is higher and the encoding is more secure.Comment: 7 pages (7 figures) RevTeX, Please e-mail Lakshmanan for figures,
submitted to Phys. Lett. A (E-mail: [email protected]
Rich Variety of Bifurcations and Chaos in a Variant of Murali-Lakshmanan-Chua Circuit
A very simple nonlinear parallel nonautonomous LCR circuit with Chua's diode
as its only nonlinear element, exhibiting a rich variety of dynamical features,
is proposed as a variant of the simplest nonlinear nonautonomous circuit
introduced by Murali, Lakshmanan and Chua(MLC). By constructing a two-parameter
phase diagram in the plane, corresponding to the forcing amplitude
(F) and frequency , we identify, besides the familiar period-doubling
scenario to chaos, intermittent and quasiperiodic routes to chaos as well as
period-adding sequences, Farey sequences, and so on. The chaotic dynamics is
verified by both experimental as well as computer simulation studies including
PSPICE.Comment: 4 pages, RevTeX 4, 5 EPS figure
Generating Finite Dimensional Integrable Nonlinear Dynamical Systems
In this article, we present a brief overview of some of the recent progress
made in identifying and generating finite dimensional integrable nonlinear
dynamical systems, exhibiting interesting oscillatory and other solution
properties, including quantum aspects. Particularly we concentrate on Lienard
type nonlinear oscillators and their generalizations and coupled versions.
Specific systems include Mathews-Lakshmanan oscillators, modified Emden
equations, isochronous oscillators and generalizations. Nonstandard Lagrangian
and Hamiltonian formulations of some of these systems are also briefly touched
upon. Nonlocal transformations and linearization aspects are also discussed.Comment: To appear in Eur. Phys. J - ST 222, 665 (2013
Conjugate coupling induced symmetry breaking and quenched oscillations
Spontaneous symmetry breaking (SSB) is essential and plays a vital role many
natural phenomena, including the formation of Turing pattern in organisms and
complex patterns in brain dynamics. In this work, we investigate whether a set
of coupled Stuart-Landau oscillators can exhibit spontaneous symmetry breaking
when the oscillators are interacting through dissimilar variables or conjugate
coupling. We find the emergence of SSB state with coexisting distinct dynamical
states in the parametric space and show how the system transits from symmetry
breaking state to out-of-phase synchronized (OPS) state while admitting
multistabilities among the dynamical states. Further, we also investigate the
effect of feedback factor on SSB as well as oscillation quenching states and we
point out that the decreasing feedback factor completely suppresses SSB and
oscillation death states. Interestingly, we also find the feedback factor
completely diminishes only symmetry breaking oscillation and oscillation death
(OD) states but it does not affect the nontrivial amplitude death (NAD) state.
Finally, we have deduced the analytical stability conditions for in-phase and
out-of-phase oscillations, as well as amplitude and oscillation death states.Comment: Accepted for publication in Europhysics Letter
Extended Prelle-Singer Method and Integrability/Solvability of a Class of Nonlinear th Order Ordinary Differential Equations
We discuss a method of solving order scalar ordinary differential
equations by extending the ideas based on the Prelle-Singer (PS) procedure for
second order ordinary differential equations. We also introduce a novel way of
generating additional integrals of motion from a single integral. We illustrate
the theory for both second and third order equations with suitable examples.
Further, we extend the method to two coupled second order equations and apply
the theory to two-dimensional Kepler problem and deduce the constants of motion
including Runge-Lenz integral.Comment: 18 pages, Article dedicated to Professor F. Calogero on his
70thbirthda
Enhanced synchronization in an array of spin torque nano oscillators in the presence of oscillating external magnetic field
We demonstrate that the synchronization of an array of electrically coupled
spin torque nano-oscillators (STNO) modelled by
Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation can be enhanced appreciably
in the presence of a common external microwave magnetic field. The applied
microwave magnetic field stabilizes and enhances the regions of synchronization
in the parameter space of our analysis, where the oscillators are exhibiting
synchronized oscillations thereby emitting improved microwave power. To
characterize the synchronized oscillations we have calculated the locking range
in the domain of external source frequency.Comment: Accepted for publication in Europhysics Letters (EPL
On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator
Using the modified Prelle- Singer approach, we point out that explicit time
independent first integrals can be identified for the damped linear harmonic
oscillator in different parameter regimes. Using these constants of motion, an
appropriate Lagrangian and Hamiltonian formalism is developed and the resultant
canonical equations are shown to lead to the standard dynamical description.
Suitable canonical transformations to standard Hamiltonian forms are also
obtained. It is also shown that a possible quantum mechanical description can
be developed either in the coordinate or momentum representations using the
Hamiltonian forms.Comment: 19 page
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