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dc.contributor.authorWilson, Marcus T.
dc.contributor.authorSteyn-Ross, Moira L.
dc.contributor.authorSteyn-Ross, D. Alistair
dc.contributor.authorSleigh, James W.
dc.contributor.authorGillies, Iain-Patrick
dc.contributor.authorHailstone, David J.
dc.date.accessioned2010-03-19T03:32:59Z
dc.date.available2010-03-19T03:32:59Z
dc.date.issued2010
dc.identifier.citationWilson, M. T., Steyn-Ross, D. A., Steyn-Ross, M. L., Sleigh, J. W., Gillies, I.-P. & Hailstone, D. J. (2010). What can a mean-field model tell us about the dynamics of the cortex?. In D. A. Steyn-Ross & M. Steyn-Ross (Eds), Modeling Phase Transitions in the Brain. (pp. 223-242). New York, USA: Springer.en
dc.identifier.isbn978-1-4419-0795-0
dc.identifier.urihttps://hdl.handle.net/10289/3739
dc.description.abstractIn this chapter we examine the dynamical behavior of a spatially homogeneous two-dimensional model of the cortex that incorporates membrane potential, synaptic flux rates and long- and short-range synaptic input, in two spatial dimensions, using parameter sets broadly realistic of humans and rats. When synaptic dynamics are included, the steady states may not be stable. The bifurcation structure for the spatially symmetric case is explored, identifying the positions of saddle–node and sub- and supercritical Hopf instabilities. We go beyond consideration of small-amplitude perturbations to look at nonlinear dynamics. Spatially-symmetric (breathing mode) limit cycles are described, as well as the response to spatially-localized impulses. When close to Hopf and saddle–node bifurcations, such impulses can cause traveling waves with similarities to the slow oscillation of slow-wave sleep. Spiral waves can also be induced. We compare model dynamics with the known behavior of the cortex during natural and anesthetic-induced sleep, commenting on the physiological significance of the limit cycles and impulse responses.en
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherSpringeren_NZ
dc.relation.urihttp://www.springerlink.com/content/k63874264291kp5p/?p=034b995cb9794ea390a004bc563ad842π=4en
dc.rightsThis is an author’s accepted version of an article published in the book: Modeling Phase Transitions in the Brain. © 2010 Springer Science+Business Media, LLC.en
dc.subjectcortical modelen
dc.subjectinstabilityen
dc.subjectbifurcationen
dc.subjectlimit cycleen
dc.subjectanesthesiaen
dc.subjectsleepen
dc.subjectk-complexen
dc.titleWhat can a mean-field model tell us about the dynamics of the cortex?en
dc.typeChapter in Booken
dc.identifier.doi10.1007/978-1-4419-0796-7_10en
dc.relation.isPartOfModeling Phase Transitions in the Brainen_NZ
pubs.begin-page223en_NZ
pubs.elements-id9176
pubs.end-page241en_NZ


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