Synchronization and Phase Ordering in Globally Coupled Chaotic Maps

  • O. Alvarez-LlamozaEmail author
  • M. G. Cosenza
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 112)


We investigate the processes of synchronization and phase ordering in a system of globally coupled maps possessing bistable, chaotic local dynamics. The stability boundaries of the synchronized states are determined on the space of parameters of the system. The collective properties of the system are characterized by means of the persistence probability of equivalent spin variables that define two phases, and by a magnetization-like order parameter that measures the phase-ordering behavior. As a consequence of the global interaction, the persistence probability saturates for all values of the coupling parameter, in contrast to the transition observed in the temporal behavior of the persistence in coupled maps on regular lattices. A discontinuous transition from a nonordered state to a collective phase-ordered state takes place at a critical value of the coupling. On an interval of the coupling parameter, we find three distinct realizations of the phase-ordered state, which can be discerned by the corresponding values of the saturation persistence. Thus, this statistical quantity can provide information about the transient behaviors that lead to the different phase configurations in the system. The appearance of disordered and phase-ordered states in the globally coupled system can be understood by calculating histograms and the time evolution of local map variables associated to the these collective states.


Coupling Strength Coupling Parameter Collective Behavior Spin Variable Chaotic Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work is supported by project No. C-1906-14-05-B from CDCHTA, Universidad de Los Andes, Venezuela. O. A. thanks Projet Prometeo, Secretaría de Educación Superior, Ciencia, Tecnología e Innovación, Senescyt, Ecuador. M. G. C. is grateful to the Senior Associates Program of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Departamento de FísicaFACYT, Universidad de CaraboboValenciaVenezuela
  2. 2.Centro de Física FundamentalUniversidad de Los AndesMéridaVenezuela
  3. 3.Universidad Católica de CuencaCuencaEcuado

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