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Excitable pulses are among the most widespread dynamical patterns that occurin many different systems, ranging from biological cells to chemical reactionsand ecological populations. Traditionally, the mutual annihilation of twocolliding pulses is regarded as their prototypical signature. Here we show thatcolliding excitable pulses may exhibit soliton-like crossover and pulsenucleation if the system obeys a mass conservation constraint. In contrast toprevious observations in systems without mass conservation, these alternativecollision scenarios are robustly observed over a wide range of parameters. Wedemonstrate our findings using a model of intracellular actin waves since, ontime scales of wave propagations over the cell scale, cells obey theconservation of actin monomers. The results provide a key concept to understandthe ubiquitous occurrence of actin waves in cells, suggesting why they are socommon, and why their dynamics is robust and long-lived.

Excitable solitons: Annihilation, crossover, and nucleation of pulses in mass-conserving activator-inhibitor media