A quasi-periodic route to chaos in a parametrically driven nonlinear medium
| Autor: | J A Vélez, Marcel G. Clerc, Ronald Rivas, Ana M. Cabanas, Harald Pleiner, L.M. Pérez, Boris A. Malomed, Pablo Díaz, David Laroze |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
J.2 General Mathematics Applied Mathematics Chaotic General Physics and Astronomy FOS: Physical sciences Statistical and Nonlinear Physics Lyapunov exponent Pattern Formation and Solitons (nlin.PS) Nonlinear Sciences - Chaotic Dynamics Instability Nonlinear Sciences - Pattern Formation and Solitons Standing wave 35Q55 symbols.namesake Amplitude Nonlinear medium symbols Statistical physics Parametric oscillator Chaotic Dynamics (nlin.CD) Bifurcation |
| Popis: | 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. to be published in Chaos, Solitons & Fractals |
| Databáze: | OpenAIRE |
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