Nucleation and propagation of excitation fronts in self-excited systems

The paper considers the transition between spatially localized and propagating stick–slip motion in frictional systems. To overcome the difficulties related to the non-smoothness of the friction law we have studied two models: a friction-excited chain of weakly coupled oscillators excited by a frictional moving belt (model I) and a chain of Van der Pol oscillators (model II). The two models show very similar dynamical features. Both exhibit discrete breathers (i.e. spatially localized periodic solutions) for low coupling. For higher coupling, both exhibit propagation of switch fronts from low to high-amplitude limit cycle oscillations. Besides, in both models the transition from discrete breathers to propagating limit cycles happens through a nucleation process and, above a certain critical coupling, the velocity of propagation scales linearly with the elastic coupling coefficient. We suggest that dynamical features similar to what was demonstrated in this work are expected for models that are different quantitatively but preserve the same structure of the state space in every single unit.