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 and Boris A. Malomed

Chaos, Solitons & Fractals, 2021, vol. 151, issue C

Abstract: 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.

Keywords: Parametric forcing; Dissipative systems; Pendula chain; Chaos; Lyapunov exponents (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921004434

DOI: 10.1016/j.chaos.2021.111089

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