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

Year: 2023

Authors: Ciszak M., Balle S., Piro O., Marino F.

Autors Affiliation: Ist Nazl Ottica, CNR, Via Sansone 1, I-50019 Sesto Fiorentino, Italy; Inst Mediterrani Estudis Avancats, Dept Ecol & Marine Resources, IMEDEA, CSIC,UIB, Esporles, Spain; Univ Illes Balears, Dept Fis, Km 7-5, E-07122 Palma De Mallorca, Spain; Sez Firenze, INFN, Via Sansone 1, I-50019 Sesto Fiorentino, Italy.

Abstract: The van der Pol-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 van der Pol-FitzHugh-Nagumo model driven by noise, the inter-spike 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 times in the nearly-periodic firing state, obey the same scaling law – as a function of the control parameter – than the one at the onset of 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.

Journal/Review: CHAOS SOLITONS & FRACTALS

Volume: 167      Pages from: 113053-1  to: 113053-10

KeyWords: Mixed-mode oscillations
DOI: 10.1016/j.chaos.2022.113053

Citations: 3
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