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An analytical study in coupled map lattices of synchronized states and traveling waves, and of their period-doubling cascades

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  • Herrera, Ma Dolores Sotelo
  • Martín, Jesús San

Abstract

Several theorems are demonstrated that determine sufficient conditions for the existence of synchronized states (both periodical and chaotic) and also of traveling waves in a CML. The existence of period-doubling cascades for the described patterns are also established. Thus, many numerical procedures in CML are given rigorous mathematical foundations. Furthermore, numerical results in CML published to date, are much more general than previously thought.

Suggested Citation

  • Herrera, Ma Dolores Sotelo & Martín, Jesús San, 2009. "An analytical study in coupled map lattices of synchronized states and traveling waves, and of their period-doubling cascades," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 901-910.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:901-910
    DOI: 10.1016/j.chaos.2009.02.040
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    References listed on IDEAS

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    1. Palaniyandi, P. & Muruganandam, P. & Lakshmanan, M., 2008. "Coexistence of synchronized and desynchronized patterns in coupled chaotic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 991-1018.
    2. San Martín, Jesús & Rodríguez-Pérez, Daniel, 2009. "Conjugation of cascades," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 666-681.
    3. Li, Ping & Li, Zhong & Halang, Wolfgang A. & Chen, Guanrong, 2007. "Li–Yorke chaos in a spatiotemporal chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 335-341.
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    Cited by:

    1. Khellat, Farhad & Ghaderi, Akashe & Vasegh, Nastaran, 2011. "Li–Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 934-939.

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