Intermittent chaotic spiking in the van der Pol-FitzHugh-Nagumo system with inertia

TL;DR

This paper investigates chaotic mixed-mode dynamics in a 3D FitzHugh-Nagumo neuron model with inertia, revealing intermittent transitions to chaos and scaling laws similar to type I intermittency near bifurcations.

Contribution

It demonstrates the emergence of intermittent chaotic spiking in a 3D neuron model with inertia and links it to bifurcation theory, extending understanding beyond standard 2D models.

Findings

Chaotic mixed-mode states with irregular interspike intervals.

Intermittent transitions to chaos follow a scaling law akin to type I intermittency.

Correspondence between residence times and bifurcation dynamics.

Abstract

The three-dimensional (3D) Fitzhugh-Nagumo neuron model with inertia was shown to exhibit a chaotic mixed-mode dynamics composed of large-amplitude spikes separated by an irregular number of small-amplitude chaotic oscillations. In contrast to the standard 2D Fitzhugh-Nagumo model driven by noise, the interspike-intervals distribution displays a complex arrangement of sharp peaks related to the unstable periodic orbits of the chaotic attractor. For many ranges of parameters controlling the excitability of the system, we observe that chaotic mixed-mode states consist of lapses of nearly regular spiking interleaved by others of highly irregular one. We explore here the emergence of these structures and show their correspondence to the intermittent transitions to chaos. In fact, the average residence time in the nearly-periodic firing state, obeys the same scaling law -- as a function of the control parameter -- than the one at the onset type I intermittency for dynamical systems in the vicinity of a saddle node bifurcation. We hypothesize that this scenario is also present in a variety of slow-fast neuron models characterized by the coexistence of a two-dimensional fast manifold and a one-dimensional slow one.