ArticleJournal of mathematical neuroscience2012
Dynamical systems analysis of spike-adding mechanisms in transient bursts.
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 10 papers.
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Who cites it
10 citing papers in PubMed.
- Dendritic interaction of timescales in afterdepolarization potentials and nonmonotonic spike-adding.Journal of computational neuroscience · 2026Article
- Article
- The Na+/K+-ATPase generically enables deterministic bursting in class I neurons by shearing the spike-onset bifurcation structure.PLoS computational biology · 2024Article
- Classification of bursting patterns: A tale of two ducks.PLoS computational biology · 2022Review
- Somatostatin-Positive Interneurons Contribute to Seizures inThe Journal of neuroscience : the official journal of the Society for Neuroscience · 2021Article
- Canard solutions in neural mass models: consequences on critical regimes.Journal of mathematical neuroscience · 2021Article
- Methods to assess binocular rivalry with periodic stimuli.Journal of mathematical neuroscience · 2020Article
- 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
- Understanding Epileptiform After-Discharges as Rhythmic Oscillatory Transients.Frontiers in computational neuroscience · 2017Article
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Authors and funding
3 authors.
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Abstract
Transient bursting behaviour of excitable cells, such as neurons, is a common feature observed experimentally, but theoretically, it is not well understood. We analyse a five-dimensional simplified model of after-depolarisation that exhibits transient bursting behaviour when perturbed with a short current injection. Using one-parameter continuation of the perturbed orbit segment formulated as a well-posed boundary value problem, we show that the spike-adding mechanism is a canard-like transition that has a different character from known mechanisms for periodic burst solutions. The biophysical basis of the model gives a natural time-scale separation, which allows us to explain the spike-adding mechanism using geometric singular perturbation theory, but it does not involve actual bifurcations as for periodic bursts. We show that unstable sheets of the critical manifold, formed by saddle equilibria of the system that only exist in a singular limit, are responsible for the spike-adding transition; the transition is organised by the slow flow on the critical manifold near folds of this manifold. Our analysis shows that the orbit segment during the spike-adding transition includes a fast transition between two unstable sheets of the slow manifold that are of saddle type. We also discuss a different parameter regime where the presence of additional saddle equilibria of the full system alters the spike-adding mechanism.
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