MR2997965 (Review) 37D45Viana, R. L.; Lopes, S. R.;Szezech, J.D., Jr.; Caldas, I. L.Synchronization of chaos and the transition to wave turbulence.Internat. J. Bifur. Chaos Appl. Sci. Engrg. 22 (2012), no. 10, 1250234, 9 pp.1793-6551

In this paper the authors analyze the onset of the wave turbulence in the spatially extended threewaveinteracting model by using the concept of synchronization. In order to work with a setof ordinary differential equations, they make a pseudo-spectral decomposition of the wave fieldand identify the onset of wave turbulence as the excitation of spatial modes in the presence ofunderlying temporally chaotic dynamics. Each spatial point is regarded as a nonlinear oscillatorand the onset of wave turbulence is the point where the oscillators lose phase synchronization.The authors use an extremely sensitive complex-order parameter to estimate the threshold of weakturbulence and perform a Lyapunov analysis leading to the detection of the so-called blowoutbifurcation.