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Related Experiment Videos

Multirhythmic bursting.

Robert J. Butera1

  • 1Mathematical Research Branch, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, 9190 Wisconsin Avenue, Suite 350, Bethesda, Maryland 20814.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
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Multiple concentric limit cycles in bursting neuron models arise from systems with at least two slow variables. This study reveals criteria for multistability in neuronal bursting dynamics.

Area of Science:

  • Computational Neuroscience
  • Dynamical Systems Theory
  • Mathematical Biology

Background:

  • A complex bursting neuron model exhibits seven coexisting limit cycle solutions.
  • These unique solutions are concentric in the slow variable space.
  • Previous work identified these complex behaviors in specific models.

Purpose of the Study:

  • To investigate the origin of multiple concentric limit cycles in bursting neuron models.
  • To identify the minimal model requirements for such multistability.
  • To establish criteria for generating multiple stable concentric limit cycles.

Main Methods:

  • Utilized a minimal 4-variable bursting cell model.
  • Constructed Poincaré maps via saddle-node bifurcations of fast subsystems.

Related Experiment Videos

  • Decomposed Poincaré maps into active and silent phase submaps.

    • Main Results:

    • Identified parameter spaces exhibiting single, multiple, and chaotic limit cycles.
    • Defined a threshold between active and silent phases using bifurcations.
    • Demonstrated that multistability requires at least two slow variables.

    Conclusions:

    • Established necessary criteria for bursting models to possess multiple stable concentric limit cycles.
    • Validated these criteria in a generalized 3-variable model.
    • Showed that such multistability is not possible in models with only one slow variable.