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One- and two-cluster synchronized dynamics of non-diffusively coupled Tchebycheff map networks

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  • Schäfer, Mirko
  • Greiner, Martin

Abstract

We use the master stability formalism to discuss one- and two-cluster synchronization of coupled Tchebycheff map networks. For diffusively coupled map systems, the one-cluster synchronized dynamics is given by the behaviour of the individual maps, and the coupling only determines the stability of the coherent state. For the case of non-diffusive coupling and for two-cluster synchronization, the synchronized dynamics on networks is different from the behaviour of the single individual map. Depending on the coupling, we study numerically the characteristics of various forms of the resulting synchronized dynamics. The stability properties of the respective one-cluster synchronized states are discussed for arbitrary network structures. For the case of two-cluster synchronization on bipartite networks we also present analytical expressions for fixed points and zig-zag patterns, and explicitly determine the linear stability of these orbits for the special case of ring-networks.

Suggested Citation

  • Schäfer, Mirko & Greiner, Martin, 2012. "One- and two-cluster synchronized dynamics of non-diffusively coupled Tchebycheff map networks," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 825-837.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:6:p:825-837
    DOI: 10.1016/j.chaos.2012.02.017
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    References listed on IDEAS

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    1. Rech, Paulo C. & Beims, Marcus W. & Gallas, Jason A.C., 2007. "Generation of quasiperiodic oscillations in pairs of coupled maps," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1394-1410.
    2. Rech, Paulo C. & Beims, Marcus W. & Gallas, Jason A.C., 2004. "Naimark–Sacker bifurcations in linearly coupled quadratic maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 351-355.
    3. Schäfer, Mirko & Greiner, Martin, 2011. "Disordered chaotic strings," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 93-97.
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    1. Rech, Paulo C. & Beims, Marcus W. & Gallas, Jason A.C., 2007. "Generation of quasiperiodic oscillations in pairs of coupled maps," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1394-1410.
    2. Rech, Paulo C., 2009. "A coupling of three quadratic maps," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1949-1952.

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