Dispersion relations to oscillatory reaction-diffusion systems with the self-consistent flow

Dispersion curves to a oscillatory reaction-diffusion system with the selfconsistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point of inflection which separates the dispersion curves into two branches corresponding to trigger and phase waves, moves according to the value of the advection constant. The dynamics of phase wave in reactiondiffusion-advection equations has been studied by limit cycle perturbations. The dispersion relation obtained from the phase equation shows that the competition between diffusion and advection constants modulates the oscillation frequency from the bulk oscillation in the long-wave dynamics. Such a competition implies that phase waves with the flow have a wider variety of dynamics than waves without the flow. 47.70.Fw, 87.17.Aa, 87.18.Pj Typeset using REVTEX Present address: Research Institute for Electronic Science, Hokkaido University, Sapporo, 0600812, JAPAN