Modelling wave propagation across a series of gaps

Abstract

Wave propagation across a series of gaps in a one-dimensional excitable medium is simulated using the Oregonator model of the Belousov–Zhabotinsky reaction. In agreement with recent experiments, we observe features such as the critical gap width W_cr, critical spacing between gaps S_cr and frequency transformation of the passage of a train of waves across a gap with width W ≤ W_cr. The role of activator kinetics in the gap is studied and the effect of excitability (through variation of parameters f and ε) on the fraction of waves which successfully cross the domain is determined. We also find that the probability of a wave successfully propagating through the entire domain decreases with increasing number of gaps, and the profile of the activator species is examined for evidence of a “weakening” effect in a multiple gap system.