Phase Description of Stable Limit-cycle Solutions in Reaction-diffusion Systems

Phase reduction theory for stable limit-cycle solutions of one-dimensional reaction-diffusion systems is developed. By locally approximating the isochrons of the limit-cycle orbit, we derive the phase sensitivity function, which is a key quantity in the phase description of limit cycles. As an example, synchronization of traveling pulses in a pair of mutually interacting reaction-diffusion systems is analyzed. It is shown that the traveling pulses can exhibit multi–modal phase locking.