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

TL;DR

This paper explores a novel route to spatiotemporal chaos in a parametrically driven nonlinear medium, revealing a quasiperiodic transition from standing waves to chaos through bifurcation analysis.

Contribution

It introduces a new understanding of chaos emergence in extended nonlinear systems via a quasiperiodic route starting from the sine-Gordon model.

Findings

Identification of quasiperiodic route to chaos in a driven nonlinear chain

Bifurcation diagrams illustrating transition from standing waves to chaos

Analysis of dynamical regimes using Lyapunov exponents and power spectra

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 quasiperiodic 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.