• Transition of phase order in coupled map systems

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      https://www.ias.ac.in/article/fulltext/pram/095/0096

    • Keywords

       

      Logistic map; dark lines; cobweb diagram; time correlation of direction phase

    • Abstract

       

      By studying the time series of logistic maps, dark lines in bifurcation diagrams and cobweb diagrams, characteristics of sequential iterations of the map are found. Before merging together two chaotic bands, sequential iterations of the map present an ordered state. After that, with the instability of the hyperstable periodic orbit, sequential iterations of the map appear disordered. Therefore, the statistical results of time correlation of direction phase are introduced to describe the transition of the collective behaviour. Based on the two-dimensional coupled map lattice, the relationship between bifurcation parameters and order parameters with the change of coupling strength is studied. We show that when the coupling strength is weak, the critical bifurcation parameters are positively correlated with the coupling strength. When the coupling strength is large, the phase order of the system is not affected by the coupling strength. The transition of collective behaviour in a modular network is also studied. By fixing modularity and bifurcation parameters, with the change of coupling strength, the collective behaviour presents a transition process from spatiotemporal chaos to phase-ordered state. There are periodic orbits in the spatiotemporal chaotic region. A phase synchronisation region can be present in the antiphase synchronisation region. Furthermore, there exist multistable solutions in the region.

    • Author Affiliations

       

      BIN ZHANG1 2 JUN LIU2 SHI-XIAN QU1

      1. School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, China
      2. Computer College, Weinan Normal University, Weinan 714099, China
    • Dates

       
  • Pramana – Journal of Physics | News

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