Chemical Waves and the Diffusive Coupling of Limit Cycle Oscillators

We analyze a model of an oscillating chemical reaction taking place in a diffusive medium. Using singular perturbation techniques, we derive a nonlinear equation that determines how spatial variations in the phase of the oscillations evolve in time. This result is the key to understanding the propagation of chemical waves. In particular, we use it to account for certain experimental observations on the Belusov–Zhabotinskii reaction.