Propagation of fronts in activator-inhibitor systems with a cutoff

We consider a two-component system of reaction-diffusion equations with a small cutoff in the reaction term. A semi-analytical solution of fronts and how the front velocities vary with the parameters are given for the case when the system has a piecewise linear nonlinearity. We find the existence of a nonequilibrium Ising-Bloch bifurcation for the front speed when the cutoff is present. Numerical results of solutions to these equations are also presented and they allow us to consider the collision between fronts, and the existence of different types of traveling waves emerging from random initial conditions.