In this talk, we establish the rigorous existence of fast traveling pulse solutions in a modified three-component Belousov–Zhabotinsky reaction–diffusion system. We prove the coexistence of two distinct traveling pulses with different wave speeds. In particular, when the equilibrium loses hyperbolicity, we apply the center manifold Theory to reduce the system and analyze the resulting dynamics. The trajectory of the traveling pulse passes through a turning point, and the phenomenon of delay of stability loss caused by the turning point requires the use of the Exchange lemma for the turning points.