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Managing heterogeneity in the study of neural oscillator dynamics

Author(s): Laing, CR; Zou, Yu; Smith, B; Kevrekidis, Yannis G.

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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. © 2012 Laing et al.
Publication Date: 1-Jan-2012
Citation: Laing, CR, Zou, Y, Smith, B, Kevrekidis, YG. (2012). Managing heterogeneity in the study of neural oscillator dynamics. Journal of Mathematical Neuroscience, 2 (1), 10.1186/2190-8567-2-5
DOI: doi:10.1186/2190-8567-2-5
EISSN: 2190-8567
Pages: 1 - 22
Type of Material: Journal Article
Journal/Proceeding Title: Journal of Mathematical Neuroscience
Version: Final published version. This is an open access article.

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