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

Stochastic resonance with different periodic forces in overdamped two coupled anharmonic oscillators

We study the stochastic resonance phenomenon in the overdamped two coupled anharmonic oscillators with Gaussian noise and driven by different external periodic forces. We consider (i) sine, (ii) square, (iii) symmetric saw-tooth, (iv) asymmetric saw-tooth, (v) modulus of sine and (vi) rectified sinusoidal forces. The external periodic forces and Gaussian noise term are added to one of the two state variables of the system. The effect of each force is studied separately. In the absence of noise term, when the amplitude $f$ of the applied periodic force is varied cross-well motion is realized above a critical value ($f_{\mathrm{c}}$) of $f$. This is found for all the forces except the modulus of sine and rectified sinusoidal forces.Stochastic resonance is observed in the presence of noise and periodic forces. The effect of different forces is compared. The logarithmic plot of mean residence time $\tau_{\mathrm{MR}}$ against $1/(D - D_{\mathrm{c}})$ where $D$ is the intensity of the noise and $D_{\mathrm{c}}$ is the value of $D$ at which cross-well motion is initiated shows a sharp knee-like structure for all the forces. Signal-to-noise ratio is found to be maximum at the noise intensity $D=D_{\mathrm{max}}$ at which mean residence time is half of the period of the driving force for the forces such as sine, square, symmetric saw-tooth and asymmetric saw-tooth waves. With modulus of sine wave and rectified sine wave, the $SNR$ peaks at a value of $D$ for which sum of $\tau_{MR}$ in two wells of the potential of the system is half of the period of the driving force. For the chosen values of $f$ and $\omega$, signal-to-noise ratio is found to be maximum for square wave while it is minimum for modulus of sine and rectified sinusoidal waves.Comment: 13 figures,27 page

Markov Chain Monte Carlo: Can We Trust the Third Significant Figure?

Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the quality of the reported estimates. We address this issue in that we discuss why Monte Carlo standard errors are important, how they can be easily calculated in Markov chain Monte Carlo and how they can be used to decide when to stop the simulation. We compare their use to a popular alternative in the context of two examples.Comment: Published in at http://dx.doi.org/10.1214/08-STS257 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org