Excitability in a model with a saddle-node homoclinic bifurcation (Q1431450)

A system is called extended if it consists of many individual similar subsystems distributed in space, and all the subsystems have the same dynamics. The authors are interested in the emergence of collective behaviour of an extended system when the initial conditions of a local subsystem are changed. When the local dynamics has a stable steady state in the phase space is close to a homoclinic orbit, the authors show that in the extended system wave trains, propagating solitary pulses and propagating pulse packets can develop. These types of wave patterns depend on the distribution of the initial states of the extended system.