Fig. 19

The emergence of a turbulent phase state in a phase oscillator continuum model. The parameters are those as in Fig. 18 with \(\omega=0\) for which \(\alpha=0.63\), \(\beta =5.16\) and \(\gamma=0.096\). The physical domain size is 2⁷ and we have used a numerical mesh of 2¹² points with Matlab ode45 to evolve Eq. (43) with convolutions computed using fast Fourier transforms. As an order parameter describing the system we have chosen \(|\varPsi|\), where \(\varPsi= (\epsilon_{1} W_{1}+\epsilon_{2} W_{2} )\otimes z + \epsilon_{3} W_{3} \otimes z^{2}\)