Pulse dynamics in a reaction–diffusion system

We formulate a theory for pulse dynamics in an excitable reaction–diffusion system not only in one dimension but also in higher dimensions. In the singular limit where the width of pulse boundaries is infinitesimally thin, we derive the equation of motion for a pair of interacting pulses (spots in higher dimensions). This equation exhibits a bifurcation that a motionless pulse loses stability and begins to propagate. An inertia term appears which originates from a time-delayed interaction between pulses mediated by slow diffusion of the inhibitor. By employing the analogy of particle motion in a conserved system, we can clarify the mechanism that the pulses undergo an elastic-like collision in a special parameter regime as observed by computer simulations even though the system is purely dissipative.