Neural spike renormalization. Part I - Universal number 1

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

For a class of circuit models for neurons, it has been shown that the transmembrane electrical potentials in spike bursts have an inverse correlation with the intra-cellular energy conversion: the fewer spikes per burst the more energetic each spike is. Here we demonstrate that as the per-spike energy goes down to zero, a universal constant to the bifurcation of spike-bursts emerges in a similar way as Feigenbaum's constant does to the period-doubling bifurcation to chaos generation, and the new universal constant is the first natural number 1.

Original languageEnglish (US)
Pages (from-to)2940-2957
Number of pages18
JournalJournal of Differential Equations
Volume250
Issue number6
DOIs
StatePublished - Mar 15 2011

Keywords

  • Circuit models of neurons
  • Feigenbaum constant
  • Isospiking bifurcation
  • Period-doubling bifurcation
  • Poincaré return maps
  • Renormalization universality

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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