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dc.contributor.authorWilson, Marcus T.
dc.contributor.authorSteyn-Ross, D. Alistair
dc.contributor.authorSteyn-Ross, Moira L.
dc.contributor.authorSleigh, James W.
dc.coverage.spatialConference held at University of Adelaide, South Australiaen_NZ
dc.date.accessioned2014-03-03T02:13:45Z
dc.date.available2014-03-03T02:13:45Z
dc.date.issued2008
dc.identifier.citationWilson, M. T., Steyn-Ross, D. A., Steyn-Ross, M. L., & Sleigh, J. W. (2008). Describing the stochastic dynamics of neurons using Hamilton’s equations of classical mechanics. In Proceedings of the Australian Institute of Physics 18th National Congress, 30 November-5 December 2008, Adelaide, Australia.en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/8538
dc.description.abstractWe consider the most likely behaviour of neuron models by formulating them in terms of Hamilton’s equations. Starting from a Lagrangian for a stochastic system, we describe how Hamilton’s equations of classical mechanics can be used to derive an equivalent description in terms of canonical co-ordinates and momenta. We give physical meaning to these generalized momenta; specifically they are linear combinations of the noise terms in the stochastic model. Pseudo-kinetic energy and potential energy terms are also derived. The conjugate momenta can be considered as growing modes, and by implication the most likely noise input to a system will grow exponentially at large times; this surprising prediction agrees with existing experimental work on a single neuron. For many-neuron models, multiple growing modes will exist, and the numerical analysis of these is more complicated; however, the approach may still provide insight on the more detailed dynamics of these systems.en_NZ
dc.format.mimetypeapplication/pdf
dc.language.isoenen_NZ
dc.publisherAustralian Institute of Physicsen_NZ
dc.relation.urihttp://www.aip.org.au/info/sites/default/files/Congress2008/AIPC2008/PDF/AUTHOR/AP081190.PDFen_NZ
dc.rightsThis article has been published in proceedings of the Australian Institute of Physics 18th National Congress. © 2008 AIP.en_NZ
dc.subjectneuronsen_NZ
dc.subjectmodellingen_NZ
dc.subjectHamilton’s equationsen_NZ
dc.subjectbrain dynamicsen_NZ
dc.titleDescribing the stochastic dynamics of neurons using Hamilton’s equations of classical mechanicsen_NZ
dc.typeConference Contributionen_NZ
dc.relation.isPartOfAustralian Institute of Physics 18th National Congressen_NZ
pubs.begin-page1en_NZ
pubs.elements-id18395
pubs.end-page4en_NZ
pubs.finish-date2008-12-05en_NZ
pubs.start-date2008-11-30en_NZ


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