dc.contributor.author | Wilson, Marcus T. | |
dc.contributor.author | Steyn-Ross, D. Alistair | |
dc.contributor.author | Steyn-Ross, Moira L. | |
dc.contributor.author | Sleigh, James W. | |
dc.coverage.spatial | Conference held at University of Adelaide, South Australia | en_NZ |
dc.date.accessioned | 2014-03-03T02:13:45Z | |
dc.date.available | 2014-03-03T02:13:45Z | |
dc.date.issued | 2008 | |
dc.identifier.citation | Wilson, 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.uri | https://hdl.handle.net/10289/8538 | |
dc.description.abstract | We 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.mimetype | application/pdf | |
dc.language.iso | en | en_NZ |
dc.publisher | Australian Institute of Physics | en_NZ |
dc.relation.uri | http://www.aip.org.au/info/sites/default/files/Congress2008/AIPC2008/PDF/AUTHOR/AP081190.PDF | en_NZ |
dc.rights | This article has been published in proceedings of the Australian Institute of Physics 18th National Congress. © 2008 AIP. | en_NZ |
dc.subject | neurons | en_NZ |
dc.subject | modelling | en_NZ |
dc.subject | Hamilton’s equations | en_NZ |
dc.subject | brain dynamics | en_NZ |
dc.title | Describing the stochastic dynamics of neurons using Hamilton’s equations of classical mechanics | en_NZ |
dc.type | Conference Contribution | en_NZ |
dc.relation.isPartOf | Australian Institute of Physics 18th National Congress | en_NZ |
pubs.begin-page | 1 | en_NZ |
pubs.elements-id | 18395 | |
pubs.end-page | 4 | en_NZ |
pubs.finish-date | 2008-12-05 | en_NZ |
pubs.start-date | 2008-11-30 | en_NZ |