Observers design for a new weakly coupled map function

Sebastien Hénaff (1) , Ina Taralova (1) , René Lozi (2)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 JAD - Laboratoire Jean Alexandre Dieudonné

In some engineering applications, such as chaotic encryption, chaotic maps have to exhibit required statistical and spectral properties close to those of random signals. However, most of the papers dealing with synchronization and observer synthesis consider maps exhibiting poor statistical and spectral properties. Moreover, most of the time these properties, however essential for the chaotic encryption, are simply neglected. Unlike these papers, in our work we present the analysis of a new ultra weakly coupled maps system introduced by Lozi. The model is a deterministic one, but exhibits spectral properties (spectrum, correlation and autocorrelation) close to those of random signals, and successfully passed all the statistical tests for closeness to random signals (NIST). Two different observers have been designed. The convergence rate has been discussed in the case of affine maps, and the conditions to decrease the convergence rate by a factor of 16 have been presented, based on the locally linear behaviour of the weakly coupled map.

Mots clés: chaos; identifiability; observer; synchronisation

Domaines: Systèmes dynamiques [math.DS]

Sebastien Hénaff, Ina Taralova, René Lozi. Observers design for a new weakly coupled map function. ICCSA 2009 The 3rd International Conference on Complex Systems and Applications, Jun 2009, Le Havre, France. pp.47-50. ⟨hal-00368576⟩