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This paper is concerned with the existence and qualitative properties ofpulsating fronts for spatially periodic reaction-diffusion equations withbistable nonlinearities. We focus especially on the influence of the spatialperiod and, under various assumptions on the reaction terms and by usingdifferent types of arguments, we show several existence results when thespatial period is small or large. We also establish some properties of the setof periods for which there exist non-stationary fronts. Furthermore, we provethe existence of stationary fronts or non-stationary partial fronts at anyperiod which is on the boundary of this set. Lastly, we characterize the signof the front speeds and we show the global exponential stability of thenon-stationary fronts for various classes of initial conditions.

Bistable pulsating fronts for reaction-diffusion equations in a periodic habitat