ArticleJournal of mathematical neuroscience2012
A showcase of torus canards in neuronal bursters.
Article in Journal of mathematical neuroscience, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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Who cites it
6 citing papers in PubMed.
- Article
- Classification of bursting patterns: A tale of two ducks.PLoS computational biology · 2022Review
- Canard solutions in neural mass models: consequences on critical regimes.Journal of mathematical neuroscience · 2021Article
- Canard-induced complex oscillations in an excitatory network.Journal of mathematical biology · 2020Article
- Saddle Slow Manifolds and Canard Orbits in [Formula: see text] and Application to the Full Hodgkin-Huxley Model.Journal of mathematical neuroscience · 2018Article
- Eupnea, tachypnea, and autoresuscitation in a closed-loop respiratory control model.Journal of neurophysiology · 2017Article
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Authors and funding
5 authors.
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Abstract
Rapid action potential generation - spiking - and alternating intervals of spiking and quiescence - bursting - are two dynamic patterns commonly observed in neuronal activity. In computational models of neuronal systems, the transition from spiking to bursting often exhibits complex bifurcation structure. One type of transition involves the torus canard, which we show arises in a broad array of well-known computational neuronal models with three different classes of bursting dynamics: sub-Hopf/fold cycle bursting, circle/fold cycle bursting, and fold/fold cycle bursting. The essential features that these models share are multiple time scales leading naturally to decomposition into slow and fast systems, a saddle-node of periodic orbits in the fast system, and a torus bifurcation in the full system. We show that the transition from spiking to bursting in each model system is given by an explosion of torus canards. Based on these examples, as well as on emerging theory, we propose that torus canards are a common dynamic phenomenon separating the regimes of spiking and bursting activity.
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