Stability of negative-image equilibria in spike-timing-dependent plasticity

We investigate the stability of negative image equilibria in mean synaptic weight dynamics governed by spike-timing-dependent plasticity (STDP). The model architecture closely follows the anatomy and physiology of the electrosensory lateral line lobe (ELL) of mormyrid electric fish. The ELL uses a spike-timing-dependent learning rule to form a negative image of the reafferent signal from the fish's own electric discharge, thus improving detectability of external electric fields. We derive sufficient conditions for existence of the negative image and necessary and sufficient conditions for stability, for arbitrary postsynaptic potential functions and arbitrary learning rules. This significantly generalizes earlier investigations. We then apply the general result to several examples of biological interest, including a class of learning rules consistent with the rule observed experimentally in the mormyrid ELL.