Mass-conservation sets excitable pulse collisions to be spatiotemporal organizing centers

Outcomes of propagating pulse collisions are of fundamental importance in many fields, ranging from physiology to industrial devices. Pulses are traditionally classified as solitons if upon collision they behave as particles, or excitable-pulses if they annihilate each other. Collisions in a non-equilibrium system with mass conservation, a common property of natural systems, exhibit rich dynamics that range from soliton-like to annihilation, and even nucleation of new pulses post-collision. Mass-conservation is shown to be a key ingredient for this behavior to occur robustly over a wide range of parameters. As such, collisions can be considered as organizing centers, for example, in intracellular actin waves.