The evolution of travelling waves from chemical-clock reactions

A clock-reaction is a chemical reaction which gives rise to an initial indu ction period before a significant change in concentration of one of the che mical species occurs. In this paper the development of travelling waves fro m a particular class of inhibited autocatalytic clock-reactions is analysed . The numerical solutions show that, after the induction period, a propagat ing reaction-diffusion front is initiated. This front is seen to accelerate initially and then to become a constant-speed travelling wave. An asymptot ic analysis of the large-time travelling-wave behaviour is given and from t his it is possible to fix a minimum wave speed. The asymptotic predictions of the wave speed are found to agree well with those of the numerical solut ion.