  We study the dynamics of a damped harmonic oscillator in the presence of a
retarded potential with state-dependent time-delayed feedback. In the limit of
small time-delays, we show that the oscillator is equivalent to a Li\'enard
system. This allows us to analytically predict the value of the first Hopf
bifurcation, unleashing a self-oscillatory motion. We compute bifurcation
diagrams for several model parameter values and analyse multistable domains in
detail. Using the Lyapunov energy function, two well-resolved energy levels
represented by two coexisting stable limit cycles are discerned. Further
exploration of the parameter space reveals the existence of a superposition
limit cycle, encompassing two degenerate coexisting limit cycles at the
fundamental energy level. When the system is driven very far from equilibrium,
a multiscale strange attractor displaying intrinsic and robust intermittency is
uncovered.
