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

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