Bistable reaction-diffusion systems can have robust zero-velocity fronts

We show that for a class of bistable reaction-diffusion systems, zero-velocity fronts can be robust in the singular limit where one of the diffusion coefficients vanishes. In this case, stationary fronts can persist along variations of the system parameters. This property contrasts with the standard result that the front velocity v(μ), expressed as a function of a control parameter μ, is zero only at some isolated values μ 0 , and thus not giving robustness to zero-velocity fronts when μ is varied.