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

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

Chaos, Solitons & Fractals, 2024, vol. 186, issue C

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.

Keywords: Faraday patterns; Spatiotemporal chaos; Lyapunov spectrum (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077924007963
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924007963

DOI: 10.1016/j.chaos.2024.115244

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().