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      https://www.ias.ac.in/article/fulltext/pram/070/03/0417-0438

    • Keywords

       

      Synchronization; coupled maps; dynamical systems; Bose-Mesner algebra.

    • Abstract

       

      By choosing a dynamical system with 𝑑 different couplings, one can rearrange a system based on the graph with a given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a relation between the vertexes. Based on the $E_{0}$ transverse projection operator, we addressed synchronization problem of an array of the linearly coupled map lattices of identical discrete time systems. The synchronization rate is determined by the second largest eigenvalue of the transition probability matrix. Algebraic properties of the Bose-Mesner algebra with an associated scheme with definite spectrum has been used in order to study the stability of the coupled map lattice. Associated schemes play a key role and may lead to analytical methods in studying the stability of the dynamical systems. The relation between the coupling parameters and the chaotic region is presented. It is shown that the feasible region is analytically determined by the number of couplings (i.e. by increasing the number of coupled maps, the feasible region is restricted). It is very easy to apply our criteria to the system being studied and they encompass a wide range of coupling schemes including most of the popularly used ones in the literature.

    • Author Affiliations

       

      M A Jafarizadeh1 2 3 S Behina4 E Faizi1 3 S Ahadpour1 3

      1. Department of Theoretical Physics and Astrophysics, Tabriz University, Tabriz 51664, Iran
      2. Institute for Studies in Theoretical Physics and Mathematics, Tehran 19395-1795, Iran
      3. Research Institute for Fundamental Sciences, Tabriz 51664, Iran
      4. Department of Physics, Islamic Azad University, Urmia, Iran
    • Dates

       
  • Pramana – Journal of Physics | News

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