Control of Spiral Instabilities in Reaction-Diffusion Systems

Abstract

Spiral instabilities and their controls are investigated in a reaction-diffusion system using the Belousov-Zhabotinsky reaction. Two spiral instabilities, the long-wavelength in- stability and the Doppler instability, are reported, which can lead to spatiotemporal chaos. The long-wavelength instability occurs in an oscillatory regime, while the Doppler instabil- ity occurs in an excitable regime. To control these two instabilities, two different strategies are proposed according to their defect-generating mechanisms. For the long-wavelength in- stability in an oscillatory system, the control can be achieved by introducing a local pace- maker, which emits stable traveling waves to sweep off the unstable spiral defects. For the Doppler instability, the control can be achieved by trapping the spiral tip with a local area of higher diffusion coefficient than its surroundings.