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

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2024, Volume and Issue: 34(5)

Published: May 1, 2024

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

Language: Английский

Strong symmetry breaking rhythms created by folded nodes in a pair of symmetrically coupled, identical Koper oscillators

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2024, Volume and Issue: 34(5)

Published: May 1, 2024

The Koper model is a prototype system with two slow variables and one fast variable that possesses small-amplitude oscillations (SAOs), large-amplitude (LAOs), mixed-mode (MMOs). In this article, we study pair of identical oscillators are symmetrically coupled. Strong symmetry breaking rhythms presented the types SAO-LAO, SAO-MMO, LAO-MMO, MMO-MMO, in which simultaneously exhibit different types. We identify key folded nodes serve as primary mechanisms responsible for strong nature breaking. maximal canards these guide orbits through neighborhoods points. For all present, exhibited by separated phase space oscillator.

Language: Английский

Canards dynamics to explore the rhythm transition under electromagnetic induction

Chaos Solitons & Fractals, Journal Year: 2023, Volume and Issue: 169, P. 113304 - 113304

Published: March 1, 2023

Language: Английский