Bifurcation analysis of bistable oscillator dynamics for human hair-cell bundle structures by mapping the Floquet multipliers

초록

This study presents an initial study on the bifurcation analysis of bistable oscillator dynamics for human hair-cell bundle structures. The hair-cell bundles within the human cochlea possess highly nonlinear stiffness while sound transmission. To better understand this bistable oscillator dynamics, this study focused on the bifurcation phenomena using the Floquet theory. To define the bifurcations associated with super- and sub-harmonic resonances, the harmonic balance method (HBM) was first utilized with Hill's method, for determining the dynamics stability conditions. In addition, the Floquet multipliers were mapped to examine their relationship with the bifurcation characteristics. To examine the bifurcation characteristics, only the Floquet multipliers associated with unstable conditions were selected because those associated with stable conditions were decaying terms. Then, the complex values of the Floquet multipliers at specific frequency locations were compared with the bifurcations' characteristics. When numerically calculated bifurcations were compared with the results obtained using the HBM, mapping the Floquet multipliers was sufficient for predicting the bifurcations of a biomimetic system inspired by the hair-cell bundle structure. This study suggests practical techniques for employing the HBM with Hill's method by mapping the Floquet multipliers to investigate complex nonlinearities that occur in bistable-stiffness systems.

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