Mixed-mode oscillations in a three-timescale coupled Morris–Lecar system

Phan, Ngoc Anh; Wang, Yangyang

doi:10.1063/5.0181308

Title: Mixed-mode oscillations in a three-timescale coupled Morris–Lecar system

Journal Article · 07 May 2024 · Chaos: An Interdisciplinary Journal of Nonlinear Science

DOI: https://doi.org/10.1063/5.0181308 · OSTI ID:2470358

^[1];

^[2]

University of Iowa, Iowa City, IA (United States)
Brandeis University, Waltham, MA (United States)

Mixed-mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. It is well known that MMOs in two-timescale systems can arise either from a canard mechanism associated with folded node singularities or a delayed Andronov–Hopf bifurcation (DHB) of the fast subsystem. While MMOs in two-timescale systems have been extensively studied, less is known regarding MMOs emerging in three-timescale systems. In this work, we examine the mechanisms of MMOs in coupled Morris–Lecar neurons with three distinct timescales. We investigate two kinds of MMOs occurring in the presence of a singularity known as canard-delayed-Hopf (CDH) and in cases where CDH is absent. In both cases, we examine how features and mechanisms of MMOs vary with respect to variations in timescales. Our analysis reveals that MMOs supported by CDH demonstrate significantly stronger robustness than those in its absence. Moreover, we show that the mere presence of CDH does not guarantee the occurrence of MMOs. This work yields important insights into conditions under which the two separate mechanisms in two-timescale context, canard and DHB, can interact in a three-timescale setting and produce more robust MMOs, particularly against timescale variations.

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Research Organization:: Brandeis University, Waltham, MA (United States)

Sponsoring Organization:: USDOE; National Institutes of Health (NIH)

OSTI ID:: 2470358

Journal Information:: Chaos: An Interdisciplinary Journal of Nonlinear Science, Journal Name: Chaos: An Interdisciplinary Journal of Nonlinear Science Journal Issue: 5 Vol. 34; ISSN 1054-1500

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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