ABSTRACT
To our knowledge, the earliest attempt to model the skipping phenomenon can be found in the seminal work of Gerstein and Mandelbrot (1964). Their random walk integrate-and-fire (IF) model could generate peaks at integer multiples of the driving period when the parameter controlling the deterministic drift toward threshold was periodically modulated, simulating the action of auditory tone bursts (clicks) on the auditory fibers. Weiss (1966) has also proposed, as part of a model of the auditory periphery, a model neuron (intended to represent VIIIth nerve neurons) which is driven by the output of the transducer (i.e., the hair cell generator potential) as well as by gaussian noise. This model has a refractory period but no spiking mechanism per se (i.e., it is an IF model). It reproduces some of the features of multimodal ISIHs in response to fast auditory clicks ( :::::: 0.1 ms) presented at a slow rate. The intervals between peaks were determined by the oscillatory impulse response functions of the cochlear partition at the location of the hair cell which connects to the fiber. Below we focus on a general simple model of sensory neurons with sinusoidal stimulation (rather than periodic clicks) at various driving periods (greater than the refractory period) where skipping is observed. The phase-locking dynamics of biological oscillators has attracted much attention, especially when a steady entrainment pattern (e.g., m firings occurring during n cycles of the stimulus) is observed experimentally. However, Glass et al. (1980) have studied the phase-locking dynamics of a simple IF model with noise and have found unstable zones with no phase-locking in between regions 'of phase space with stable phase-locking
patterns. For low-amplitude periodic inputs, their model yielded quasi-periodic dynamics, while patterns with irregular skipped or intercalated beats were seen at higher amplitudes.
