Affiliation:
1. Bogolyubov Institute for Theoretical Physics, Kyiv, Ukraine
Abstract
Firing statistics of excitatory binding neuron (BN) is considered. The neuron is driven externally by a Poisson stream. Influence of feedback, which conveys every output impulse to the input with time delay , on the statistics of output spikes is studied. The resulting output stream is not Poissonian, and the authors obtain its inter-spike intervals (ISI) distribution for the case of BN, BN with instantaneous, , and delayed, , feedback. Output statistics of neuron with delayed feedback differs essentially from that found for the case of no feedback as well as from the case of instantaneous feedback. ISI distributions, found for delayed feedback, are characterized with jumps, derivative discontinuities and include -function type singularity. Also, for non-zero refractory time, the authors obtain multiple-ISI conditional probability density and prove, that delayed feedback presence results in non-Markovian statistics of neuronal firing. It is concluded, that delayed feedback presence can radically change neuronal firing statistics.