Complex Dynamics of Nonlinear Oscillations of Hair Bundles of Auditory Hair Cell Regulated by Memristor

The nonlinear oscillations of hair bundles of auditory hair cell are important for sound perception. Memristors, as electronic components highly similar to the behavior of neurons and synapses, show potential in neuromodulation. The present paper, for the first time, introduces memristors into the regulation of hair bundle mechanical vibrations, constructs a dynamical model with memristor coupling, and investigates the regulatory dynamics of coupling strength (γ) on oscillation modes through simulation and bifurcation analysis. The results show that as γ increases, the hair bundle oscillation patterns exhibit a variety of complex patterns, including different types of spiking, bursting, and chaos. Bifurcation analysis and Lyapunov exponents validate the dynamic process of mode transitions, indicating that memristors influence oscillation patterns by regulating the adaptation force of hair bundle. Moreover, bifurcation analysis in the two-parameter plane indicates that increasing γ can expand the oscillation region of the hair bundle, but excessive coupling can suppress oscillations. Under specific parameter combinations, the system exhibits insensitivity to memristor regulation, reflecting the robustness of the auditory system. This study provides a theoretical basis for understanding the nonlinear characteristics of auditory function and developing novel neuromodulation technologies.