Various coherence resonances and fast-slow dynamics of bursting/spiking patterns in auditory hair bundles

The ability to perceive a specific sound from complex background noise in auditory system is termed the cocktail party problem, with the mechanism remaining not fully clear. The problem may be related to the exogenous noise-induced stochastic oscillations of hair bundle in the auditory hair cell, which is the initial stage of auditory perception. In the present paper, different coherence resonances (CRs) evoked from different deterministic oscillations of hair bundle are identified. Firstly, transitions between different oscillations modulated by calcium, i.e., from high resting state, to bursting, to chaos, to spiking, and to low resting state, are reproduced in a parameter plane. Secondly, different oscillations are distinguished with codimension-1 and -2 bifurcations of fast subsystem, acquired with fast-slow analysis. Notably, the bursting exhibits novel dynamics, running around saddle and unstable limit cycle originating from Hopf bifurcation instead of around the well-known stable limit cycle. Finally, the exogenous noise induces different CRs from the different oscillations. With increasing noise intensity, anti-CR and CR appears for bursting, double CRs at low and high frequencies for chaos, CR for low and high quiescent states, and Non-CR for spiking. Various CRs arise from stochastic shifts between distinct behaviors around bifurcations of fast subsystem. The double CRs and the transition from anti-CR to CR extend the conditions and manifestations of CR, and suggest the frequency and intensity detection of auditory system. The complex dynamics offer a potential peripheral mechanism for the cocktail party problem, which aids in modulations of hearing function and bionic auditory technologies.