  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.
