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Mixed-mode oscillations in a three-timescale coupled Morris-Lecar system
Ngoc Anh Phan1, Yangyang Wang2
1Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, USA.
Chaos (Woodbury, N.Y.)
|May 8, 2024
Summary
Mixed-mode oscillations (MMOs) in three-timescale systems are more robust with a canard-delayed-Hopf (CDH) singularity. Understanding these complex dynamics reveals how canard and delayed Andronov-Hopf bifurcation mechanisms interact.
Area of Science:
- Computational Neuroscience
- Dynamical Systems Theory
- Nonlinear Dynamics
Background:
- Mixed-mode oscillations (MMOs) are complex behaviors in multi-timescale systems, characterized by alternating large and small amplitude oscillations.
- In two-timescale systems, MMOs commonly arise from canard mechanisms or delayed Andronov-Hopf bifurcations (DHBs).
- MMOs in three-timescale systems remain less understood compared to their two-timescale counterparts.
Purpose of the Study:
- To investigate the mechanisms underlying MMOs in coupled Morris-Lecar neurons with three distinct timescales.
- To analyze MMOs in the presence and absence of a canard-delayed-Hopf (CDH) singularity.
- To explore the influence of timescale variations on MMO features and mechanisms.
Main Methods:
- Numerical simulations of coupled Morris-Lecar neuron models with three distinct timescales.
- Analysis of MMOs in the presence of a canard-delayed-Hopf (CDH) singularity.
- Comparative study of MMOs with and without CDH, examining robustness against timescale variations.
Main Results:
- MMOs supported by the CDH singularity exhibit significantly greater robustness compared to those without it.
- The presence of CDH alone does not guarantee the occurrence of MMOs.
- Variations in timescales impact the features and underlying mechanisms of MMOs.
Conclusions:
- The interaction between canard and DHB mechanisms in three-timescale systems can produce more robust MMOs, especially against timescale variations.
- CDH singularities play a crucial role in enhancing the robustness of MMOs in complex neural systems.
- This study provides critical insights into the conditions favoring robust MMOs in multi-timescale neuronal dynamics.
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