Pulse–pulse interaction in reaction–diffusion systems

It had been long believed that one-dimensional travelling pulses and the corresponding two-dimensional expanding rings and spiral waves arising in excitable reaction–diffusion systems annihilate when they closely approach one another. However, recently it has been numerically confirmed that if the velocity is very slow, expanding rings and spiral do not necessarily annihilate. In particular, in some situation, two closely approaching pulses reflect, as if they were elastic like objects. By using the center manifold theory, we show that if there are travelling pulses which primarily and super-critically bifurcate from a standing pulse when some parameter is varied, they possess reflection mechanism if the velocity is very slow.