Nucleation and propagation of excitation fronts in self-excited systems

Abstract: Frictional interfaces exhibits a very rich dynamical behavior due to frictional interactions. This work focuses on the transition between spatially localized and propagating stick-slip motion. To overcome the difficulties related to the non-smoothness of the friction law we have studied two models: (model I) a friction-excited chain of weakly coupled oscillators excited by a frictional moving belt and (model II) a chain of Van der Pol oscillators. The two models show very similar dynamical features. Both exhibit discrete breathers (i.e. spatially localized periodic solutions) solutions for low coupling and show propagation along the chain of high amplitude limit cycles for stronger elastic coupling between the unit cells. 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 single-unit topology.