Kinetic theory for neuronal networks with fast and slow excitatory conductances driven by the same spike train

Aaditya V. Rangan, Gregor Kovačič, David Cai

Research output: Contribution to journalArticlepeer-review

Abstract

We present a kinetic theory for all-to-all coupled networks of identical, linear, integrate-and-fire, excitatory point neurons in which a fast and a slow excitatory conductance are driven by the same spike train in the presence of synaptic failure. The maximal-entropy principle guides us in deriving a set of three (1+1) -dimensional kinetic moment equations from a Boltzmann-like equation describing the evolution of the one-neuron probability density function. We explain the emergence of correlation terms in the kinetic moment and Boltzmann-like equations as a consequence of simultaneous activation of both the fast and slow excitatory conductances and furnish numerical evidence for their importance in correctly describing the coarse-grained dynamics of the underlying neuronal network.

Original languageEnglish (US)
Article number041915
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume77
Issue number4
DOIs
StatePublished - Apr 18 2008

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Fingerprint Dive into the research topics of 'Kinetic theory for neuronal networks with fast and slow excitatory conductances driven by the same spike train'. Together they form a unique fingerprint.

Cite this