This paper presents a monolithic implementation of a cryptosystem based on the Corron and Hahs scheme [ I ] . The baseband chaotic encryptioddecryption system has been designed at the transistor level and fabricated using the AMI 1.2pm CMOS technology available through the MOSIS foundry. While the mathematical model of the Lorenz system is straightforward, its silicon implementation is not. Typ...

This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display (i) two 1-scroll chaotic attractors simultaneously, with only three equilibria, and (ii) two 2-scroll chaotic attractors simultaneously, with five equilibria. Several issues such as some basic dynamical behaviors, routes to chaos, bifurcations, periodic windo...

The Lorenz attractor was introduced in 1963 by E. N. Lorenz as one of the first examples of strange attractors. However Lorenz’ research was mainly based on (non-rigourous) numerical simulations and, until recently, the proof of the existence of the Lorenz attractor remained elusive. To address that problem some authors introduced geometric Lorenz models and proved that geometric Lorenz models ...

We comment on mathematical results about the statistical behavior of Lorenz equations an its attractor, and more generally to the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer assi...

Continuing the discussion of the multi-adaptive Galerkin methods mcG(q) and mdG(q) presented in [A. Logg, SIAM J. Sci. Comput., 24 (2003), pp. 1879–1902], we present adaptive algorithms for global error control, iterative solution methods for the discrete equations, features of the implementation Tanganyika, and computational results for a variety of ODEs. Examples include the Lorenz system, th...

Based on the invariance principle of differential equations, a simple adaptive-feedback scheme is proposed to strictly synchronize almost all chaotic systems. Unlike the usual linear feedback, the variable feedback strength is automatically adapted to completely synchronize two almost arbitrary identical chaotic systems, so this scheme is analytical, and simple to implement in practice. Moreove...

A nonlinear evolution system constructed from the Lorenz system is solved numerically by a parallelized predictor-corrector method. The numerical solution of such system reveals the details of interactions between dissipation and ellipticity and it may lead to better understanding of instability in some physical systems. Our algorithm and its implementation for solving this system is of general...

It came as a surprise to most scientists when Lorenz in 1963 discovered chaos in a simple system of three autonomous ordinary differential equations with two quadratic nonlinearities. This paper reviews efforts over the subsequent years to discover even simpler examples of chaotic flows. There is reason to believe that the algebraically simplest examples of chaotic flows with quadratic and piec...

Constantin, Foais and Gibbon proved that the laser equations (Lorenz PDE) define a dynamical system in L2 with a C∞ attractor. We extend this theorem to show that the attractor is contained in every Gevrey class, G , for 1 < s < ∞. This demonstrates a remarkable smoothing mechanism for this hyperbolic system. We consider the consequences of this theorem for finitedimensionality of the dynamics....

Mobile robotics, after decades of continuous development, keeps up as an intensive research issue because of its ever-increasing application to different domains and its economical and technological relevance. Interesting applications can be seen in robots performing floor-cleaning tasks, executing industrial transportation, exploring volcanoes, scanning areas to find explosive devices, and so ...