Global Contraction and Symmetry-Breaking Thresholds in a Reduced Fluid–Structure Vestibular Model

This preprint revisits the reduced fluid–structure model for the semicircular canal derived by Chico‑Vázquez, Moulton and Vella (J. Fluid Mech., 2025) and provides a rigorous dynamical-systems backbone for the three flow regimes they identified. Using a scalar specialisation of a general contraction inequality previously developed for plasma dynamics, the paper proves that the reduced cupular pressure equation is globally exponentially contracting under fixed head motion, with an explicit contraction rate. An exact convolution solution is derived and used to obtain small‑ and large‑stiffness asymptotics that quantitatively explain the transition from velocity‑tracking to acceleration‑tracking response. Finally, an inequality comparing the symmetric leading axial flow to asymmetric corrections yields a stiffness-dependent threshold above which asymmetric flow components dominate, giving a quantitative condition for the onset of symmetry breaking without any loss of well‑posedness.