Dynamics and stability of a discrete breather in a harmonically excited chain with vibro-impact on-site potential

TL;DR

This paper studies the existence and stability of discrete breathers in a harmonically excited chain with vibro-impact on-site potentials, revealing that adding harmonic potentials can significantly enhance breather stability.

Contribution

It provides an analytical and numerical analysis showing how harmonic on-site potentials extend breather stability domains in parameter space.

Findings

Adding harmonic on-site potential increases breather stability.

Stability domains are expanded near the anti-continuum limit.

Bifurcation scenarios are characterized analytically and numerically.

Abstract

We investigate the existence and stability of discrete breathers in a chain of masses connected by linear springs and subjected to vibro-impact on-site potentials. The latter are comprised of harmonic springs and rigid constraints limiting the possible motion of the masses. Local dissipation is introduced through a non-unit restitution coefficient characterizing the impacts. The system is excited by uniform time-periodic forcing. The present work is aimed to study the existence and stability of similar breathers in the space of parameters, if additional harmonic potentials are introduced. Existence-stability patterns of the breathers in the parameter space and possible bifurcation scenarios are investigated analytically and numerically. In particular, it is shown that the addition of harmonic on-site potential can substantially extend the stability domain, at least close to the anti-continuum limit. This result can be treated as an increase in the robustness of the breather from the perspective of possible practical applications.