Control of spiral instabilities in reaction-diffusion systems*
Hui-Min Liao1, Min-Xi Jiang1, Xiao-Nan Wang1, Lu-Qun Zhou1, and Qi Ouyang1,2
1Department of Physics; 2Center for Theoretical Biology, Peking University, Beijing 100871, P.R. China
Abstract: Spiral instabilities and their controls are investigated in a reaction-diffusion system using the Belousov-Zhabotinsky reaction. Two spiral instabilities, the long-wavelength instability and the Doppler instability, are reported, which can lead to spatiotemporal chaos. The long-wavelength instability occurs in an oscillatory regime, while the Doppler instability 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 instability in an oscillatory system, the control can be achieved by introducing a local pacemaker, 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.
Keywords: Spiral instabilities; Belousov-Zhabotinsky reaction; long-wavelength instability; Doppler instability; reaction-diffusion.
*Paper based on a presentation at the 18th IUPAC International Conference on Chemical Thermodynamics (ICCT-2004), 17-21 August 2004, Beijing, China. Other presentations are published in this issue, pp. 1297-1444.