How synapses in the auditory system wax and wane: theoretical perspectives

Spike-timing-dependent synaptic plasticity has recently provided an account of both the acuity of sound localization and the development of temporal-feature maps in the avian auditory system. The dynamics of the resulting learning equation, which describes the evolution of the synaptic weights, is governed by an unstable fixed point. We outline the derivation of the learning equation for both the Poisson neuron model and the leaky integrate-and-fire neuron with conductance synapses. The asymptotic solutions of the learning equation can be described by a spectral representation based on a biorthogonal expansion.