Minimal Models of Bursting Neurons: How Multiple Currents, Conductances, and Timescales Affect Bifurcation Diagrams | Zendy

R. M. Ghigliazza | Zendy; Philip Holmes | Zendy

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Minimal Models of Bursting Neurons: How Multiple Currents, Conductances, and Timescales Affect Bifurcation Diagrams

Author(s) -

R. M. Ghigliazza,

Philip Holmes

Publication year - 2004

Publication title -

siam journal on applied dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.218

H-Index - 61

ISSN - 1536-0040

DOI - 10.1137/030602307

Subject(s) - bursting , bifurcation , parameter space , variable (mathematics) , central pattern generator , bifurcation diagram , computer science , stability (learning theory) , spike (software development) , biological system , duty cycle , biological neuron model , generator (circuit theory) , statistical physics , control theory (sociology) , physics , mathematics , voltage , neuroscience , artificial intelligence , mathematical analysis , artificial neural network , rhythm , nonlinear system , geometry , thermodynamics , biology , quantum mechanics , software engineering , acoustics , power (physics) , control (management) , machine learning

After reviewing the Hodgkin-Huxley ionic current formulation, we introduce a three-variable generic model of a single-compartment neuron comprising a two-dimensional fast subsystem and a very slow recovery variable. We study the effects of fast and slow currents on the existence and stability of equilibria and periodic orbits for the fast subsystem, presenting a classification of currents and de- veloping graphical tools that aid in the analysis and construction of models with specified properties. We draw on these to propose a minimal model of a bursting neuron, identifying biophysical param- eters that can shape and regulate key characteristics of the membrane voltage pattern: bursting frequency, duty cycle, spike rate, and the number of action potentials per burst. We present ad- ditional examples from the literature for comparison and illustration, and in a companion paper (SIAM J. Appl. Dyn. Syst., 3 (2004), pp. 671-700), we construct a model of an insect central pattern generator using these methods.

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