Output stream of binding neuron with delayed feedback

Abstract

A binding neuron (BN) whith delayed feedback is considered. The neuron is fed externally with a Poisson stream of intensity $\lambda$. The neuron's output spikes are fed into its input with time delay $\Delta$. The resulting output stream of the BN is not Poissonian, and we look for its interspike intervals (ISI) distribution. For BN with threshold 2 an exact mathematical expression as function of $\lambda$, $\Delta$ and BN's internal memory, $\tau$ is derived for the ISI distribution, and for higher thresholds it is found numerically. The distributions found are characterized with discontinuities of jump type, and include singularity of Dirac's $\delta$-function type. It is concluded that delayed feedback presence can radically alter neuronal output firing statistics.