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Characterization of Faraday patterns and spatiotemporal chaos in parametrically driven dissipative systems

Author

Listed:
  • Reyes, L.I.
  • Pérez, L.M.
  • Pedraja-Rejas, L.
  • Díaz, P.
  • Mendoza, J.
  • Bragard, J.
  • Clerc, M.G.
  • Laroze, D.

Abstract

In this work, we have studied numerically the dynamics of the parametrically driven damped nonlinear Schrödinger equation (PDDNLS). The PDDNLS is a universal model to describe parametrically driven systems. In particular, we have characterized stationary Faraday patterns, periodic, quasi-periodic, and spatiotemporal chaos as a function of the amplitude and the frequency of the parametric driving force. We have computed the Lyapunov spectra, the Fourier spectra, the amplitude norm, and the Kaplan–Yorke dimensions as valuable indicators for the identification of several dynamical regimes. We show that in the Faraday regime, close to the bifurcation of the trivial state, the pattern amplitude scales with power one-fourth (1/4) of the bifurcation parameter. Furthermore, we have found that the pattern wavelength decreases when the detuning parameter increases. In the case of the high dimensional spatiotemporal chaotic states, we have found that the Kaplan–Yorke dimension increases linearly with the length of the system, showing its extensive character in this dynamical regime. We have also found a transition from low to high dimensional chaos when the forcing amplitude is increased.

Suggested Citation

  • Reyes, L.I. & Pérez, L.M. & Pedraja-Rejas, L. & Díaz, P. & Mendoza, J. & Bragard, J. & Clerc, M.G. & Laroze, D., 2024. "Characterization of Faraday patterns and spatiotemporal chaos in parametrically driven dissipative systems," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924007963
    DOI: 10.1016/j.chaos.2024.115244
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    References listed on IDEAS

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    1. Cabanas, Ana M. & Rivas, Ronald & Pérez, Laura M. & Vélez, Javier A. & Díaz, Pablo & Clerc, Marcel G. & Pleiner, Harald & Laroze, David & Malomed, Boris A., 2021. "A quasi-periodic route to chaos in a parametrically driven nonlinear medium," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Cabanas, A.M. & Vélez, J.A. & Pérez, L.M. & Díaz, P. & Clerc, M.G. & Laroze, D. & Malomed, B.A., 2021. "Dissipative structures in a parametrically driven dissipative lattice: Chimera, localized disorder, continuous-wave, and staggered states," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Mikheil Kharbedia & Niccolò Caselli & Diego Herráez-Aguilar & Horacio López-Menéndez & Eduardo Enciso & José A. Santiago & Francisco Monroy, 2021. "Moulding hydrodynamic 2D-crystals upon parametric Faraday waves in shear-functionalized water surfaces," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
    4. Díaz, P. & Pérez, L.M. & Reyes, L.I. & Laroze, D. & Bragard, J., 2021. "Taming Faraday waves in binary fermionic clouds: The effect of Zeeman interaction," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
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