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Auditory Nerve Fiber Modeling: A Stochastic Melnikov Approach.

pdf icon Auditory Nerve Fiber Modeling: A Stochastic Melnikov Approach. (751 K)
Franaszek, M.; Simiu, E.

Physical Review E, Vol. 57, No. 5, 5870-5876, May 1998.


Office of Naval Research, Washington, DC


building technology; acoustical nerve; chaotic dynamics; Melnikov processes; neurons; neurophysiology; signal processing; stochastic dynamics


Well-known experiments have established two basic features of auditory nerve fiber dynamics. First, harmonic excitation with constant amplitude produces mean firing rates that are largest for excitation frequencies contained in a relatively narrow best interval; for frequencies outside that interval mean firing rates decrease until, for both low and high frequencies, they become vanishingly small. Second, white or nearly white noise excitation results in multimodal interspike interval histograms. These features suggested the development of a strongly asymmetrical bistable model to which Melnikov theory applies. We show that, unlike the Fitzhugh-Nagumo equation, such a model is capable of reproducing both basic features of the dynamics. We also show that the model is consistent with experimental results on response patterns for excitation by two harmonics in the presence of spontaneous activity. The Melnikov properties of the proposed model explain both its qualitatively satisfactory performance and its potential for stochastic resonant behavior. Numerical tests confirm the robustness of the proposed model.