MR2997965 (Review) 37D45 Viana, 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 threewave interacting model by using the concept of synchronization. In order to work with a set of ordinary differential equations, they make a pseudo-spectral decomposition of the wave field and identify the onset of wave turbulence as the excitation of spatial modes in the presence of underlying temporally chaotic dynamics. Each spatial point is regarded as a nonlinear oscillator and 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 weak turbulence and perform a Lyapunov analysis leading to the detection of the so-called blowout bifurcation.