Synchronization of extended chaotic systems

The main mechanisms leading to synchronization in chaotic extended systems with short-range interactions are revised, while novel results concerning systems with long-range coupling are presented. In particular, the chaotic synchronization of replica of coupled map lattices is considered. The spatial extension allows to interpret the synchronization transitions (STs) as nonequilibrium critical phenomena. Within this framework two different kind of continuous transitions have been identified for nearest-neighbour coupling : one ruled by linear mechanisms and one by nonlinear effects [1,2]. In the first case the ST belongs to the multiplicative noise universality class, while in the nonlinear dominated case the critical exponents coincide with those measured for directed percolation (DP) [1,3]. More recently spatially extended chaotic systems with power-law decaying interactions have been considered [4]. Also in this situation the ST appears to be continuous, while the critical indexes vary with continuity with the power law exponent characterizing the interaction. Moreover, strong numerical evidences indicate that the transition belongs to the "anomalous directed percolation" family of universality classes found for Levy-flight spreading of epidemic processes [5].



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