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Naimark–Sacker bifurcations in linearly coupled quadratic maps

Author

Listed:
  • Rech, Paulo C.
  • Beims, Marcus W.
  • Gallas, Jason A.C.

Abstract

We report exact analytical expressions locating the 0→1, 1→2 and 2→4 bifurcation curves for a prototypical system of two linearly coupled quadratic maps. Of interest is the precise location of the parameter sets where Naimark–Sacker bifurcations occur, starting from a non-diagonal period-2 orbit. This result is the key to understand the onset of synchronization in networks of quadratic maps.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:342:y:2004:i:1:p:351-355
    DOI: 10.1016/j.physa.2004.04.105
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    Cited by:

    1. 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.
    2. 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.

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