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In the present work we consider a diatomic granular crystal, consisting ofalternating aluminum and steel spheres, where the first sphere is an aluminumone. The combination of dissipation, driving of the boundary, and intrinsicnonlinearity leads to complex dynamics. Specifically, we find that theinterplay of nonlinear surface modes with modes created by the driver createthe possibility, as the driving amplitude is increased, of limit cyclesaddle-node bifurcations beyond which the dynamics of the system becomeschaotic. In this chaotic state, part of the applied energy can propagatethrough the chain. We also find that the chaotic branch depends weakly on thedriving frequency and speculate a connection between the chaotic dynamics withthe gap openings between the spheres. Finally, a reverse parametriccontinuation reveals hysteretic dynamics and the existence of an interval ofmulti-stability involving stable periodic solutions and genuinely chaotic ones.The computational identification and theoretical interpretation of thebifurcation diagram of the system is corroborated by direct experimentalmeasurements showcasing all of the above features.

Hysteresis Loops and Multi-stability: From Periodic Orbits to Chaotic Dynamics (and Back) in Diatomic Granular Crystals