Statistical and Spectral Analysis of a New Weakly Coupled Maps System Hénaff Sébastien1, Taralova Ina1, Lozi René2,* 1IRCCyN, UMR CNRS 6597, École Centrale Nantes, 1 rue de la Noë, BP, 92101, F-44321 Nantes Cedex 3, France 2Laboratoire J.A. Dieudonné, UMR CNRS 6621, Université de Nice Sophia-Antipolis, F-06108 Nice Cedex 02, France *Author for Correspondence. E-mail: r.lozi@umce.ft
Abstract The complexity of chaotic maps, exhibiting deterministic, but also stochastic features makes them very promising candidates in the rush for new and secure communication technologies. However, most of the chaotic systems proposed in the literature turned out to be unsuitable for chaotic encryption, since they don't satisfy the required spectral and statistical properties for closeness to random signals. Unlike these papers, we propose to implement the new ultra weakly coupled maps system firstly introduced by Lozi. We demonstrate that this function is highly performant, and beats most of the classically used random number generators. Next, in the context. of a master-slave synchronization, an observer is required to recover the chaotic signal (and thus, the original message). Therefore, two different piece-wise linear observers have been synthesised: a Luenberger, and an inverse lag observer, and the necessary conditions for synchronization have been derived. Finally, for the second order system it has been demonstrated that the exact synchronimtion can be achieved in two iterations for any initial conditions. AMS Subject Classification: Keywords: Top |