Managing heterogeneity in the study of neural oscillator dynamics

Carlo R. Laing, Yu Zou, Ben Smith, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

We consider a coupled, heterogeneous population of relaxation oscillators used to model rhythmic oscillations in the pre-Bötzinger complex. By choosing specific values of the parameter used to describe the heterogeneity, sampled from the probability distribution of the values of that parameter, we show how the effects of heterogeneity can be studied in a computationally efficient manner. When more than one parameter is heterogeneous, full or sparse tensor product grids are used to select appropriate parameter values. The method allows us to effectively reduce the dimensionality of the model, and it provides a means for systematically investigating the effects of heterogeneity in coupled systems, linking ideas from uncertainty quantification to those for the study of network dynamics.

Original languageEnglish (US)
Article number5
JournalJournal of Mathematical Neuroscience
Volume2
Issue number1
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Neuroscience (miscellaneous)

Keywords

  • Bifurcation
  • Computation
  • Heterogeneity
  • Model reduction
  • Neural oscillators
  • Pre-Bötzinger complex

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