1,288 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
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
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
On the complete integrability and linearization of nonlinear ordinary differential equations - Part V: Linearization of coupled second order equations
Linearization of coupled second order nonlinear ordinary differential
equations (SNODEs) is one of the open and challenging problems in the theory of
differential equations. In this paper we describe a simple and straightforward
method to derive linearizing transformations for a class of two coupled SNODEs.
Our procedure gives several new types of linearizing transformations of both
invertible and non-invertible kinds. In both the cases we provide algorithms to
derive the general solution of the given SNODE. We illustrate the theory with
potentially important examples.Comment: Accepted for publication in Proc. R. Soc. London
On the complete integrability and linearization of certain second order nonlinear ordinary differential equations
A method of finding general solutions of second-order nonlinear ordinary
differential equations by extending the Prelle-Singer (PS) method is briefly
discussed. We explore integrating factors, integrals of motion and the general
solution associated with several dynamical systems discussed in the current
literature by employing our modifications and extensions of the PS method. In
addition to the above we introduce a novel way of deriving linearizing
transformations from the first integrals to linearize the second order
nonlinear ordinary differential equations to free particle equation. We
illustrate the theory with several potentially important examples and show that
our procedure is widely applicable.Comment: Proceedings of the Royal Society London Series A (Accepted for
publication) 25 pages, one tabl
A systematic method of finding linearizing transformations for nonlinear ordinary differential equations: I. Scalar case
In this set of papers we formulate a stand alone method to derive maximal
number of linearizing transformations for nonlinear ordinary differential
equations (ODEs) of any order including coupled ones from a knowledge of fewer
number of integrals of motion. The proposed algorithm is simple,
straightforward and efficient and helps to unearth several new types of
linearizing transformations besides the known ones in the literature. To make
our studies systematic we divide our analysis into two parts. In the first part
we confine our investigations to the scalar ODEs and in the second part we
focuss our attention on a system of two coupled second order ODEs. In the case
of scalar ODEs, we consider second and third order nonlinear ODEs in detail and
discuss the method of deriving maximal number of linearizing transformations
irrespective of whether it is local or nonlocal type and illustrate the
underlying theory with suitable examples. As a by-product of this investigation
we unearth a new type of linearizing transformation in third order nonlinear
ODEs. Finally the study is extended to the case of general scalar ODEs. We then
move on to the study of two coupled second order nonlinear ODEs in the next
part and show that the algorithm brings out a wide variety of linearization
transformations. The extraction of maximal number of linearizing
transformations in every case is illustrated with suitable examples.Comment: Accepted for Publication in J. Nonlinear Math. Phys. (2012
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