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 $(F-\omega)$ plane, corresponding to the forcing amplitude (F) and frequency $(\omega)$, 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 nnth Order Ordinary Differential Equations

We discuss a method of solving $n^{th}$ 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