Noise-induced synchronization for phase turbulence
نویسنده
چکیده
Phase turbulence is suppressed by applying common noise additively to the Kuramoto-Sivashinsky type equation, and the noise-induced phase synchronization is realized. The noise strength necessary for the suppression of phase turbulence is evaluated theoretically. PACS: 05.45.+b, 05.40.+j, 02.50-r Recently, various noise effects to nonlinear systems have been studied. The response of a bistable system or an excitable system to a periodic force is enhanced by the noise effect. The stochastic resonance improves signal detection by the superposed noise [1, 2, 3]. Noise-enhanced entrainment among coupled oscillators is found experimentally in Belousov-Zhabotinsky reactions [4]. Frequency locking of noise-sustained oscillations is found in coupled excitable systems [5, 6]. A small amount of noise may change a chaotic trajectory into a rather regular trajectory, and it is called noise-induced order [7]. Common noise may induce complete synchronization for uncoupled chaotic oscillators [8, 9]. It is called noise-induced synchronization. In this paper, we apply common noise for a modified equation of the Kuramoto-Sivashinsky equation. Without the common noise, the model equation exhibits phase turbulence. Noise-induced synchronization occurs and a spatially uniform state is observed owing to the common noise. The model equation is written as φt = ω − r sinφ− μφxx − φxxxx + φx + ξ(t), (1) where φ(x, t) is a phase variable, ω > r is assumed, and ξ(t) represents spatially uniform Gaussian white noise satisfying 〈ξ(t)ξ(t)〉 = 2Dδ(t− t′).
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