Nucleation and propagation of excitation fronts in self-excited systems

TL;DR

This paper investigates how excitation fronts nucleate and propagate in self-excited systems, revealing a transition from localized to propagating motion through a nucleation process in two different models.

Contribution

It introduces two models of frictional systems exhibiting similar dynamical behaviors, demonstrating the nucleation process and linear velocity scaling in excitation front propagation.

Findings

Discrete breathers occur at low coupling.

Propagation of high amplitude limit cycles at higher coupling.

Transition involves nucleation and linear velocity scaling.

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.