Phase equation with nonlinear excitation for nonlocally coupled oscillators (Q732354)

The author derives a nonlinear excited truncated phase equation of the form \(\partial_t\psi=b_4\nabla^2\psi(\nabla\psi)^2+b_5(\nabla\psi)^4+g_1\nabla^6\psi\) from the complex Ginzburg-Landau equation, governing the dynamics of reaction-diffusion systems with nonlocal coupling. In introduction it is noted that here can arise different situations governed by other equations in dependence on the truncation order in evolution equation for the phase of oscillations in reaction-diffusion systems with oscillatory dynamics and on the behavior of evolution equation coefficients.