Gluing unstable fronts and backs together can produce stable pulses

We investigate the stability of pulses that are created at T-points in reac tion-diffusion systems on the real line. The pulses are formed by gluing un stable fronts and backs together. We demonstrate that the bifurcating pulse s can nevertheless be stable, and establish necessary and sufficient condit ions that involve only the front and the back for the stability of the bifu rcating pulses. AMS classification scheme numbers: 34L05, 35B35, 37L15.