A Discrete Time Stochastic Neural Network Model

The model in discrete time is formally stated. Illustrations are provided to help non-mathematicians see what the different entities mean. Python simulation codes are given, commented, and used to illustrate the general model behavior. Leakage—what neurophysiologists describe as membrane potential relaxation towards resting value—is introduced. We then apply our newly introduced formalism to explore an intriguing question: how quickly is the influence of a neuron onto itself, through a chain of neurons connected via excitatory synapses, lost? The Erdős–Rényi random graph is introduced and used. The first section of Appendix B provides an historical background to our discrete time model.