Chaotic synchronizations of spatially extended systems as nonequilibrium phase transitions

Abstract

Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via power-law coupling is considered. The synchronization transition is studied as a non-equilibrium phase transition, and its critical properties are analyzed at varying the spatial interaction range as well as the nonlinearity of the dynamical units composing each system. In particular, continuous and discontinuous local maps are considered. In both cases the transitions are of the second order with critical indexes varying with the exponent characterizing the interaction range. For discontinuous maps it is numerically shown that the transition belongs to the anomalous directed percolation (ADP) family of universality classes, previously identified for Lévy-flight spreading of epidemic processes. For continuous maps, the critical exponents are different from those characterizing ADP, but apart from the nearest-neighbor case, the identification of the corresponding universality classes remains an open problem. Finally, to test the influence of deterministic correlations for the studied synchronization transitions, the chaotic dynamical evolutions are substituted by suitable stochastic models. In this framework and for the discontinuous case, it is possible to derive an effective Langevin description that corresponds to that proposed for ADP.

Chaotic, informational and synchronous behaviour of multiplex networks

“…The general asymmetric configuration presents nodes in one network that can randomly connect to other nodes in the other network. The considered network configurations are models of extended space-time chaotic systems 35 36 37 38 or chemical chaos 39 40 . It is also a model for two types of structures found in real neural networks 41 .…”

Nonlinear Dynamics and Chaos: Advances and Perspectives

“…Notice that this stochastic model is even more closely related to the problem of synchronization between mutually coupled map lattices (see Refs. [35][36][37][38][39][40] for a more detailed discussion), since the assumption of a stochastic evolution is appropriate everywhere in parameter space including the critical region separating the two phases.…”

Explosive First-Order Transition to Synchrony in Networked Chaotic Oscillators

“…The last several years have also witnessed an ever-increasing interest in studying networked systems composed of nonlinear dynamical units [5], and in particular, in the emergence of synchronization phenomena [6]. Within this latter context, some advances have been made for the case of non-equilibrium synchronization transitions of chaotic systems [7,8], being, however, all the reported cases examples of second order phase transitions.…”