Fluctuation effects on chemical wave fronts

The numerical resolution of the Langevin equations, with specific internal noises deduced from master equations, exhibits two qualitatively different behaviors for the reaction-diffusion wave fronts associated with either a cubic or a quadratic chemical rate. In the case of a wave front between two stable stationary states, illustrated by the Schlogl model, the effect of fluctuations in the vicinity of a bifurcation induces perturbative deviations from the deterministic predictions on observable properties, like the propagation velocity, the profile width, and the value of the highest plateau. These deviations obey power laws that are determined. For wave fronts propagating into an unstable stationary state, such as in the Fisher model, a nonperturbative fluctuation effect on velocity and profile width is observed, in relation to the selection, in the presence of noise, of a particular solution in the continuum of linearly stable deterministic solutions.