Secure Digital Signal Transmission by Multistep Parameter Modulation and Alternative Driving of Transmitter Variables

The idea of secure communication of digital signals via chaos synchronization has been plagued by the possibility of attractor reconstruction by eavesdroppers as pointed out by Perez and Cerdeira. In this Letter, we wish to present a very simple mechanism by which this problem can be overcome, wherein the signal is transmitted via a multistep parameter modulation combined with alternative driving of different transmitter variables, which makes the attractor reconstruction impossible. The method is illustrated by means of the Lorenz system and Chua's circuit as examples.Comment: 15 pages, RevTeX, 6 eps figures, To appear in Int. J. Bifurcation and Chaos (July 2001

Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators

Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at $(mN_c+1)$-th oscillators in the ring, where $m$ is an integer and $N_c$ is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by size instability. We also demonstrate that there exists an exponential relation between the number of oscillators that can support stable synchronization in the ring with the external drive and the critical coupling strength $\epsilon_c$ with a scaling exponent $\gamma$. The critical coupling strength is calculated by numerically estimating the synchronization error and is also confirmed from the conditional Lyapunov exponents (CLEs) of the coupled systems. We find that the same scaling relation exists for $m$ couplings between the drive and the ring. Further, we have examined the robustness of the synchronous states against Gaussian white noise and found that the synchronization error exhibits a power-law decay as a function of the noise intensity indicating the existence of both noise-enhanced and noise-induced synchronizations depending on the value of the coupling strength $\epsilon$. In addition, we have found that $\epsilon_c$ shows an exponential decay as a function of the number of additional couplings. These results are demonstrated using the paradigmatic models of R\"ossler and Lorenz oscillators.Comment: Accepted for Publication in Physical Review

Event--related desynchronization in diffusively coupled oscillator models

We seek explanation for the neurophysiological phenomenon of event related desynchronization (ERD) by using models of diffusively coupled nonlinear oscillators. We demonstrate that when the strength of the event is sufficient, ERD is found to emerge and the accomplishment of a behavioral/functional task is determined by the nature of the desynchronized state. We illustrate the phenomenon for the case of limit cycle and chaotic systems. We numerically demonstrate the occurrence of ERD and provide analytical explanation. We also discuss possible applications of the observed phenomenon in real physical systems other than the brain.Comment: Accepted in Physical Review Letter

Invariant subspace method to the initial and boundary value problem of the higher dimensional nonlinear time-fractional PDEs

This paper systematically explains how to apply the invariant subspace method using variable transformation for finding the exact solutions of the (k+1)-dimensional nonlinear time-fractional PDEs in detail. More precisely, we have shown how to transform the given (k+1)-dimensional nonlinear time-fractional PDEs into (1+1)-dimensional nonlinear time-fractional PDEs using the variable transformation procedure. Also, we explain how to derive the exact solutions for the reduced equations using the invariant subspace method. Additionally, in this careful and systematic study, we will investigate how to find the various types of exact solutions of the (3+1)-dimensional nonlinear time-fractional convection-diffusion-reaction equation along with appropriate initial and boundary conditions for the first time. Moreover, the obtained exact solutions of the equation as mentioned above can be written in terms of polynomial, exponential, trigonometric, hyperbolic, and Mittag-Leffler functions. Finally, the discussed method is extended for the (k+1)-dimensional nonlinear time-fractional PDEs with several linear time delays, and the exact solution of the (3+1)-dimensional nonlinear time-fractional delay convection-diffusion-reaction equation is derived.Comment: 45 page

Nonlinear Dynamics of Moving Curves and Surfaces: Applications to Physical Systems

The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a variety of physical problems in different disciplines. Making use of the underlying geometry, one can very often relate the associated evolution equations to many interesting nonlinear evolution equations, including soliton possessing nonlinear dynamical systems. Typical examples include dynamics of filament vortices in ordinary and superfluids, spin systems, phases in classical optics, various systems encountered in physics of soft matter, etc. Such interrelations between geometric evolution and physical systems have yielded considerable insight into the underlying dynamics. We present a succinct tutorial analysis of these developments in this article, and indicate further directions. We also point out how evolution equations for moving surfaces are often intimately related to soliton equations in higher dimensions.Comment: Review article, 38 pages, 7 figs. To appear in Int. Jour. of Bif. and Chao

A Study of Dynamic Pile-Soil Interaction

The paper discusses briefly the state of art on the subject of pile dynamics including consideration of soil-pile interaction. An analytical model which gives the response of a single pile buried in a layered soil medium considering variation in soil properties in the radial direction in each layer is illustrated. The paper also presents an experimental study on a full size test pile 40 cm dia and 7 m long driven into a five layered soil stratum. The results of the analytical and experimental studies are compared and suggestions for further work are given

Effect of bio-seed priming and nano zinc oxide foliar application on quality and productivity of finger millet + greengram intercropping system

A critical stage of the plant's life cycle is germination and insufficient seedling emergence contributes to the lower productivity of finger millet. Priming improves seedling emergence, reduces stand establishment time, and improves seedling germination. There is a need to develop a new technology like Nanotechnology that can precisely detect and deliver the right amount of nutrients or other inputs to safe crops for the environment and maximising productivity. A field experiment was conducted during Kharif season to evaluate the response of effective farming practice for sole finger millet + greengram intercropping system under rainfed conditions to varied levels of bio-seed priming and foliar application of nanoparticles on crop growth and productivity. The results of the experiment revealed that finger millet (Eleusine coracana) intercropped with greengram (Vigna radiata) (2:1) had a significant level (<0.05) increase in growth and yield parameter of finger millet compared to sole finger millet. Application of Prosopis juliflora leaf extract 1 per cent alone + Foliar ZnO nanoparticle @ 500 ppm showed a significant level (<0.05) increase in growth and yield parameter like grain yield (3238.84 kg ha-1), finger millet equivalent yield (FMEY) (3483.84 kg ha-1) and straw yield (7393.83 kg ha-1) compared to Pogamia pinnata leaf extract 1% alone + Foliar ZnO nanoparticle @ 500 ppm. The present study mainly focussed on cropping system, bio seed priming, and foliar application of nano zinc oxide utilized during rainfed conditions to increase uniform germination, drought resistance and improve crop yield along with nutrient content in seeds