Oberseminar Nonlinear Dynamics

Synchronization transitions in chaotic spatially extended systems with short range interactions will be briefly reviewed [1]. In particular, we will focus on the existing analogies between out-of-equilibrium phase transitions and chaotic synchronizations. Moreover, recent developments, concerning synchronization in systems with power-law coupling, will be presented [2]. In this framework, the transitions are found to be always continuous, while the critical indexes vary with continuity with the power law exponent characterizing the interaction. For discontinuous local dynamics, numerical evidences indicate that the observed transitions belong to the "anomalous directed percolation" family of universality classes found for Levy-flight spreading of epidemic processes [3]. Instead for continuous local dynamics it is not possible to associate the transitions to previously studied crtitical phenomena [4].

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