A quasi-periodic route to chaos in a parametrically driven nonlinear medium

Ana M. Cabanas*, Ronald Rivas, Laura M. Pérez, Javier A. Vélez, Pablo Díaz, Marcel G. Clerc, Harald Pleiner, David Laroze, Boris A. Malomed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of damped nonlinear oscillators, we investigate a route to spatiotemporal chaos emerging from standing waves. The route from the stationary to the chaotic state proceeds through quasi-periodic dynamics. The standing wave undergoes the onset of oscillatory instability, which subsequently exhibits a different critical frequency, from which the complexity originates. A suitable amplitude equation, valid close to the parametric resonance, makes it possible to produce universe results. The respective phase-space structure and bifurcation diagrams are produced in a numerical form. We characterize the relevant dynamical regimes by means of the largest Lyapunov exponent, the power spectrum, and the evolution of the total intensity of the wave field.

Original languageEnglish
Article number111089
JournalChaos, Solitons and Fractals
StatePublished - Oct 2021


  • Chaos
  • Dissipative systems
  • Lyapunov exponents
  • Parametric forcing
  • Pendula chain


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