Various spontaneous oscillations and Hopf bifurcation have been observed in hair bundles of auditory hair cells, which play very important roles in the auditory function. In the present paper, the bifurcations and chaos of spontaneous oscillations of hair bundles are investigated in a theoretical model to explain the experimental observations. Firstly, the equivalent negative stiffness and symmetrical characteristic of the model are acquired. The model exhibits coexisting attractors symmetrical to each other or an attractor with symmetry by itself. The attractors include stable focus, stable periodic oscillations, and chaotic oscillations. Secondly, except for the well-known subcritical and supercritical Hopf bifurcations from the stable focus to period-1 limit cycle, the complex bifurcations of spontaneous oscillation patterns such as period-doubling bifurcation cascade to chaos and intermittency between periodic limit cycles and chaos, are observed. Various chaotic oscillations are distinguished. Lastly, a complex bifurcation process containing multiple modes of oscillations and bifurcations mentioned above is obtained, which provides the relationships between different spontaneous oscillation patterns. The results present not only the well-known Hopf bifurcation, but also the various spontaneous oscillations including periodic and chaotic patterns, which are consistent with the recent experimental results. The complex bifurcation process presents a global view of the nonlinear dynamics of complex spontaneous oscillations of hair bundles, which is very important for the auditory function.
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