Damped oscillations of the probability of random events followed by absolute refractory period: exact analytical results

Abstract

There are numerous examples of natural and artificial processes that represent stochastic sequences of events followed by an absolute refractory period during which the occurrence of a subsequent event is impossible. In the simplest case of a generalized Bernoulli scheme for uniform random events followed by the absolute refractory period, the event probability as a function of time can exhibit damped transient oscillations. Using stochastically-spiking point neuron as a model example, we present an exact and compact analytical description for the oscillations without invoking the standard renewal theory. The resulting formulas stand out for their relative simplicity, allowing one to analytically obtain the amplitude damping of the 2nd and 3rd peaks of the event probability.

Final version

References in corpus (7)

• Chimera states in a multilayer network of coupled and uncoupled neurons
• Chimera states in uncoupled neurons induced by a multilayer structure
• Quasi-Critical Brain Dynamics on a Non-Equilibrium Widom Line
• Critical behavior and synchronization of discrete stochastic phase coupled oscillators
• Stochastic Wilson-Cowan models of neuronal network dynamics with memory and delay
• Low-dimensional firing-rate dynamics for populations of renewal-type spiking neurons
• The power ratio and the interval map: spiking models and extracellular data