Control of turbulence in oscillatory reaction-diffusion systems through a combination of global and local feedback

Abstract

Global time-delay autosynchronization is known to control spatiotemporal turbulence in oscillatory reactiondiffusion systems. Here, we investigate the complex Ginzburg-Landau equation in the regime of spatiotemporal turbulence and study numerically how local or a combination of global and local time-delay autosynchronization can be used to suppress turbulence by inducing uniform oscillations. Numerical simulations show that while a purely local control is unsuitable to produce uniform oscillations, a mixed local and global control can be efficient and also able to create other patterns such as standing waves, amplitude death, or traveling waves.