Statistical and spectral analysis of a new weakly coupled maps system
Résumé
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 litterature 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 synthetized : 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 synchronization can be achieved in two iterations for any initial conditions.
Domaines
Systèmes dynamiques [math.DS]
Origine : Fichiers produits par l'(les) auteur(s)
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