In the present paper, isolated response curves in a nonlinear system consisting of two masses sliding on a horizontal guide are examined. Transverse springs are attached to one mass to provide the nonlinear restoring force, and a harmonic motion of the complete system is imposed by prescribing the displacement of their supports. Numerical simulations are carried out to study the conditions of existence of isolated solutions, their bifurcations, their merging with the main response branch and their basins of attraction. This is achieved using tools including nonlinear normal modes, energy balance, harmonic balance-based continuation and bifurcation tracking, and global analysis.

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