A simple parameter can switch between different weak-noise–induced phenomena in a simple neuron model

¹ Max-Planck-Institut für Mathematik in den Naturwissenschaften - Inselstr. 22, 04103 Leipzig, Germany
² Santa Fe Institute for the Sciences of Complexity - NM 87501, Santa Fe, USA

Received: 5 September 2017
Accepted: 23 November 2017

Abstract

In recent years, several, apparently quite different, weak-noise–induced resonance phenomena have been discovered. Here, we show that at least two of them, self-induced stochastic resonance (SISR) and inverse stochastic resonance (ISR), can be related by a simple parameter switch in one of the simplest models, the FitzHugh-Nagumo (FHN) neuron model. We consider a FHN model with a unique fixed point perturbed by synaptic noise. Depending on the stability of this fixed point and whether it is located to either the left or right of the fold point of the critical manifold, two distinct weak-noise–induced phenomena, either SISR or ISR, may emerge. SISR is more robust to parametric perturbations than ISR, and the coherent spike train generated by SISR is more robust than that generated deterministically. ISR also depends on the location of initial conditions and on the time-scale separation parameter of the model equation. Our results could also explain why real biological neurons having similar physiological features and synaptic inputs may encode very different information.