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Generation of quasiperiodic oscillations in pairs of coupled maps

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

Abstract

We investigate analytically the emergence of quasiperiodic and mode-locked states of arbitrary period in pairs of coupled maps. Quasiperiodic and mode-locked states arise from Naimark–Sacker bifurcations and exhibit very rich local dynamics. We determine analytically both states for pairs of maps under symmetric and asymmetric couplings. Lyapunov spectra, portraits in parameter-space and in phase-space are used to show the transition from quasiperiodic and from mode-locked states into chaotic states and to check the range of validity of the approximations implicit in the standard normal forms.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:4:p:1394-1410
    DOI: 10.1016/j.chaos.2006.01.091
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    1. Brock, William A. & de Fontnouvelle, Patrick, 2000. "Expectational diversity in monetary economies," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 725-759, June.
    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.
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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., 2009. "A coupling of three quadratic maps," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1949-1952.

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