Output stream of binding neuron with instantaneous feedback

The binding neuron model [A.K. Vidybida,BioSystems 48, 263 (1998)] is inspired by numerical simulation of Hodgkin-Huxley-type point neuron [A.K. Vidybida,Biol. Cybern. 74, 539 (1996)], as well as by the leaky integrate-and-fire (LIF) model [J.P. Segundo, D. Perkel, H. Wyman, H. Hegstad, G.P. Moore,Kybernetic 4, 157 (1968)]. In the binding neuron, the trace of an input is remembered for a fixed period of time after which it disappears completely. This is in the contrast with the above two models, where the postsynaptic potentials decay exponentially and can be forgotten only after triggering. The finiteness of memory in the binding neuron allows one to construct fast recurrent networks for computer modeling [A.K. Vidybida,BioSystems 71, 205 (2003)]. Recently, [A.K. Vidybida,BioSystems 89, 160 (2007)], the finiteness is utilized for exact mathematical description of the output stochastic process if the binding neuron is driven with the Poisson input stream. In this paper, it is expected that every output spike of single neuron is immediately fed back into its input. For this construction, externally fed with Poisson stream, the output stream is characterized in terms of interspike interval (ISI) probability density distribution if the neuron has threshold 2. For higher thresholds, the distribution is calculated numerically. The distributions are compared with those found for binding neuron without feedback, and for leaky integrator. It is concluded that the feedback presence can radically alter spiking statistics. Copyright Springer 2008