Output stream of binding neuron with threshold 2 stimulated with renewal process

Information is transmitted between neurons in a brain via typical electrical impulses, which are called spikes. Since the activity of biological neurons is random, the statistics of neuronal activity, namely, the time intervals between neuron-generated consecutive spikes, is studied. A neuron transforms a random stream of input impulses into another stream, the output one. The input stream is described in this paper as a renewal point process. As a neuronal model, a binding neuron with threshold 2 is considered. A relationship between the Laplace transforms of the probability density functions of the interspike intervals in the input stream of impulses and the output stream generated as a response to this stimulus has been obtained. The derived relationship enables the determination of the probability density function and all of its moments. The resulting formulas are applied to the case where the input process is the Erlang one. In the considered case, the dependence of the regularity of the neuronal activity on the input stream parameters and the physical parameters of the neuron model is found. (author)