On the application of "equation-free modelling" to neural systems

Journal of Computational Neuroscience
Carlo R Laing

Abstract

"Equation-free modelling" is a recently-developed technique for bridging the gap between detailed, microscopic descriptions of systems and macroscopic descriptions of their collective behaviour. It uses short, repeated bursts of simulation of the microscopic dynamics to analyse the effective macroscopic equations, even though such equations are not directly available for evaluation. This paper demonstrates these techniques on a variety of networks of model neurons, and discusses the advantages and limitations of such an approach. New results include an understanding of the effects of including gap junctions in a model capable of sustaining spatially localised "bumps" of activity, and an investigation of a network of coupled bursting neurons.

References

Jul 17, 2007·Journal of Computational Neuroscience·Romain BretteAlain Destexhe
Feb 26, 2010·Journal of Computational Neuroscience·Carlo R LaingIoannis G Kevrekidis
Nov 9, 2006·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·S CoombesEric Shea-Brown
Apr 2, 2009·Chaos·Carlo R Laing
Jan 26, 2010·NeuroImage·S Coombes
Dec 6, 2006·The Journal of Chemical Physics·Liang QiaoIoannis G Kevrekidis
May 16, 2018·Nature Communications·Jing MengSteven J Davis
Sep 29, 2012·Journal of Neurophysiology·Joshua I Sanders, Adam Kepecs

Citations

Aug 10, 2000·Neural Computation·C C Chow, Nancy Kopell
Jul 7, 2001·Neural Computation·Carlo R Laing, C C Chow
Oct 16, 2001·Journal of Neurophysiology·B DoironLeonard Maler
Apr 26, 2002·Neural Computation·Werner M Kistler, Wulfram Gerstner
Aug 20, 2002·Neural Computation·Nicolas Fourcaud, Nicolas Brunel
Sep 27, 2003·Neural Computation·Oren ShrikiHaim Sompolinsky
Nov 25, 2003·Neural Computation·Carlo R Laing, Andre Longtin
Dec 25, 2003·Journal of Physiology, Paris·Ray W TurnerRobert J Dunn
Oct 19, 2004·Proceedings of the National Academy of Sciences of the United States of America·Nancy Kopell, Bard Ermentrout

Related Concepts

Neural Inhibition
Neurons
Feedback - System Communication
Neural Network Simulation
Nervous System Structure
Chaos Theory
Probability
Metazoa
Gap Junctions
Neural Networks (Anatomic)

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