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Open Access Research

Managing heterogeneity in the study of neural oscillator dynamics

Carlo R Laing1*, Yu Zou2, Ben Smith13 and Ioannis G Kevrekidis2

Author Affiliations

1 Institute of Information and Mathematical Sciences, Massey University, Private Bag 102-904, North Shore Mail Centre, Auckland, 0745, New Zealand

2 Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA

3 Research Centre for Cognitive Neuroscience, Department of Psychology, University of Auckland, Private Bag 92019, Auckland, New Zealand

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The Journal of Mathematical Neuroscience 2012, 2:5  doi:10.1186/2190-8567-2-5

Published: 14 March 2012

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.

Keywords:
heterogeneity; neural oscillators; pre-Bötzinger complex; model reduction; bifurcation; computation