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