Dynamic pattern formation and collisions in networks of excitable elements

Spatially extended, excitable systems with resting, activated, and refractory states, and emergent localized propagating patterns, are widespread in nature. Here a unique type of three-state excitable network model is shown to generate such dynamic patterns with rich collective dynamics. It is shown that symmetry breaking leads to the formation of dynamical patterns, leading to a change from local subdiffusive wandering to directed superdiffusive propagation. Furthermore, the model yields a rich repertoire of collision dynamics between localized propagating patterns and between propagating patterns and the refractory wakes of others. This work is particularly motivated by recent experimental studies of neural systems that exhibit localized propagating patterns, exemplifying a far wider class of excitable systems.