ArticleDiscrete and continuous dynamical systems. Series A2012
CROSS-CURRENTS BETWEEN BIOLOGY AND MATHEMATICS: THE CODIMENSION OF PSEUDO-PLATEAU BURSTING.
Article in Discrete and continuous dynamical systems. Series A, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 15 papers.
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Who cites it
15 citing papers in PubMed.
- In vivo neural activity of electrosensory pyramidal cells: Biophysical characterization and phenomenological modeling.PLoS computational biology · 2025Article
- Bifurcations and bursting in the Epileptor.PLoS computational biology · 2024Article
- Deconstructing the integrated oscillator model for pancreatic β-cells.Mathematical biosciences · 2023Article
- Slow negative feedback enhances robustness of square-wave bursting.Journal of computational neuroscience · 2023Article
- Classification of bursting patterns: A tale of two ducks.PLoS computational biology · 2022Review
- Article
- Robust spike timing in an excitable cell with delayed feedback.Journal of the Royal Society, Interface · 2021Article
- Bursting in cerebellar stellate cells induced by pharmacological agents: Non-sequential spike adding.PLoS computational biology · 2020Article
- Fast-Slow Bursters in the Unfolding of a High Codimension Singularity and the Ultra-slow Transitions of Classes.Journal of mathematical neuroscience · 2017Article
- Nature and Consequences of Biological Reductionism for the Immunological Study of Infectious Diseases.Frontiers in immunology · 2017Review
- Multiple timescale mixed bursting dynamics in a respiratory neuron model.Journal of computational neuroscience · 2016Article
- From global to local: exploring the relationship between parameters and behaviors in models of electrical excitability.Journal of computational neuroscience · 2016Article
- Preventing Data Ambiguity in Infectious Diseases with Four-Dimensional and Personalized Evaluations.PloS one · 2016Article
- Detecting the Hidden Properties of Immunological Data and Predicting the Mortality Risks of Infectious Syndromes.Frontiers in immunology · 2016Article
- Dynamical systems analysis of spike-adding mechanisms in transient bursts.Journal of mathematical neuroscience · 2012Article
Corrections and comments
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Authors and funding
3 authors.
Funding
Abstract
A great deal of work has gone into classifying bursting oscillations, periodic alternations of spiking and quiescence modeled by fast-slow systems. In such systems, one or more slow variables carry the fast variables through a sequence of bifurcations that mediate transitions between oscillations and steady states. A rigorous classification approach is to characterize the bifurcations found in the neighborhood of a singularity; a measure of the complexity of the bursting oscillation is then given by the smallest codimension of the singularities near which it occurs. Fold/homoclinic bursting, along with most other burst types of interest, has been shown to occur near a singularity of codimension three by examining bifurcations of a cubic Liénard system; hence, these types of bursting have at most codimension three. Modeling and biological considerations suggest that fold/homoclinic bursting should be found near fold/subHopf bursting, a more recently identified burst type whose codimension has not been determined yet. One would expect that fold/subHopf bursting has the same codimension as fold/homoclinic bursting, because models of these two burst types have very similar underlying bifurcation diagrams. However, no codimension-three singularity is known that supports fold/subHopf bursting, which indicates that it may have codimension four. We identify a three-dimensional slice in a partial unfolding of a doubly-degenerate Bodganov-Takens point, and show that this codimension-four singularity gives rise to almost all known types of bursting.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.