Auditory Nerve Fiber Modeling: A Stochastic Melnikov Approach.
Auditory Nerve Fiber Modeling: A Stochastic Melnikov
Franaszek, M.; Simiu, E.
Physical Review E, Vol. 57, No. 5, 5870-5876, May 1998.
Sponsor: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.