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

Abstract: Excitable pulses are among the most widespread dynamical patterns that occur in many different systems, ranging from biological cells to chemical reactions and ecological populations. Traditionally, the mutual annihilation of two colliding pulses is regarded as their prototypical signature. Here we show that colliding excitable pulses may exhibit soliton-like crossover and pulse nucleation if the system obeys a mass conservation constraint. In contrast to previous observations in systems without mass conservation, these alternative collision scenarios are robustly observed over a wide range of parameters. We demonstrate our findings using a model of intracellular actin waves since, on time scales of wave propagations over the cell scale, cells obey the conservation of actin monomers. The results provide a key concept to understand the ubiquitous occurrence of actin waves in cells, suggesting why they are so common, and why their dynamics is robust and long-lived.