The European Physical Journal Special Topics

, Volume 222, Issue 2, pp 501–510 | Cite as

Characterizing the dynamics of coupled pendulums via symbolic time series analysis

  • G. De Polsi
  • C. Cabeza
  • A.C. Marti
  • C. Masoller
Regular Article Applications to Real World Time Series


We propose a novel method of symbolic time-series analysis aimed at characterizing the regular or chaotic dynamics of coupled oscillators. The method is applied to two identical pendulums mounted on a frictionless platform, resembling Huygens’ clocks. Employing a transformation rule inspired in ordinal analysis [C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002)], the dynamics of the coupled system is represented by a sequence of symbols that are determined by the order in which the trajectory of each pendulum intersects an appropriately chosen hyperplane in the phase space. For two coupled pendulums we use four symbols corresponding to the crossings of the vertical axis (at the bottom equilibrium point), either clock-wise or anti-clock wise. The complexity of the motion, quantified in terms of the entropy of the symbolic sequence, is compared with the degree of chaos, quantified in terms of the largest Lyapunov exponent. We demonstrate that the symbolic entropy sheds light into the large variety of different periodic and chaotic motions, with different types synchronization, that cannot be inferred from the Lyapunov analysis.


European Physical Journal Special Topic Chaotic Motion Angular Variable Large Lyapunov Exponent Symbolic Dynamics 
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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  • G. De Polsi
    • 1
  • C. Cabeza
    • 1
  • A.C. Marti
    • 1
  • C. Masoller
    • 2
  1. 1.Instituto de Física, Universidad de la RepúblicaMontevideoUruguay
  2. 2.Departament de Fisica i Enginyeria Nuclear, Universitat Politecnica de CatalunyaTerrassa, BarcelonaSpain

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