Modeling spikes in natural and social phenomena

We propose a general methodology to model natural and social phenomena characterized by stochastic dynamics in which the occurrence of random spikes can be observed. The method uses excitable dynamics in a multi-regime switching approach to describe dynamical system in which the motion randomly switches between a stable dynamics and an excited dynamics. In particular we discuss a two-regime switching model in which the stable motion is described by mean-reverting diffusion process and the occurrence of spikes is described by a stochastic FitzHugh-Nagumo model.