  In the present work we consider a diatomic granular crystal, consisting of
alternating aluminum and steel spheres, where the first sphere is an aluminum
one. The combination of dissipation, driving of the boundary, and intrinsic
nonlinearity leads to complex dynamics. Specifically, we find that the
interplay of nonlinear surface modes with modes created by the driver create
the possibility, as the driving amplitude is increased, of limit cycle
saddle-node bifurcations beyond which the dynamics of the system becomes
chaotic. In this chaotic state, part of the applied energy can propagate
through the chain. We also find that the chaotic branch depends weakly on the
driving frequency and speculate a connection between the chaotic dynamics with
the gap openings between the spheres. Finally, a reverse parametric
continuation reveals hysteretic dynamics and the existence of an interval of
multi-stability involving stable periodic solutions and genuinely chaotic ones.
The computational identification and theoretical interpretation of the
bifurcation diagram of the system is corroborated by direct experimental
measurements showcasing all of the above features.
