Nonlinear Coupling Induced Anomalous State Transfer and Complete Multistate Excitation via Adiabatic Control

We theoretically proposed and experimentally demonstrated that a nonlinear acoustic dimer system with amplitude-dependent and sign-reversible coupling exhibits unprecedented control over multistability and state selection. The engineered inter-resonator coupling κ=κ_{0}+α|ψ_{1}|^{2} yields a quintic steady-state response with at most three dynamically stable states: low (LS), intermediate (IS), and high (HS). Monotonic sweeps produce asymmetric hysteresis-LS→HS on upsweep, but HS→IS→LS on downsweep-leaving a linearly stable yet dynamically inaccessible IS under conventional driving. Basin-of-attraction analysis shows that nonlinear coupling reshapes the phase-space geometry, creating barriers that isolate the IS. Leveraging this insight, we developed a simple up-down-up adiabatic protocol that achieves full and selective access to all stable states, including the otherwise transparent IS. Mapping versus drive frequency and damping reveals transitions from separated bistable loops to a unified tristable regime. These results, to our knowledge, provide the first experimental realization of nonlinear-coupling-governed multistability and a versatile route to programmable multistate control.