Show simple item record

dc.contributor.authorKopell, Nancyen_US
dc.date.accessioned2018-10-04T17:11:51Z
dc.date.available2018-10-04T17:11:51Z
dc.identifierhttp://arxiv.org/abs/math/0305013v1
dc.identifier.citationNancy Kopell. "Rhythms of the nervous system: mathematical themes and variations." Proceedings of the ICM, v. 3, Issue 8, pp. 5 - 816.
dc.identifier.urihttps://hdl.handle.net/2144/31454
dc.description.abstractThe nervous system displays a variety of rhythms in both waking and sleep. These rhythms have been closely associated with different behavioral and cognitive states, but it is still unknown how the nervous system makes use of these rhythms to perform functionally important tasks. To address those questions, it is first useful to understood in a mechanistic way the origin of the rhythms, their interactions, the signals which create the transitions among rhythms, and the ways in which rhythms filter the signals to a network of neurons. This talk discusses how dynamical systems have been used to investigate the origin, properties and interactions of rhythms in the nervous system. It focuses on how the underlying physiology of the cells and synapses of the networks shape the dynamics of the network in different contexts, allowing the variety of dynamical behaviors to be displayed by the same network. The work is presented using a series of related case studies on different rhythms. These case studies are chosen to highlight mathematical issues, and suggest further mathematical work to be done. The topics include: different roles of excitation and inhibition in creating synchronous assemblies of cells, different kinds of building blocks for neural oscillations, and transitions among rhythms. The mathematical issues include reduction of large networks to low dimensional maps, role of noise, global bifurcations, use of probabilistic formulations.en_US
dc.format.extentp. 805-816en_US
dc.relation.ispartofProceedings of the ICM
dc.subjectDynamical systemsen_US
dc.subjectNervous systemen_US
dc.subjectMathematical themeen_US
dc.subjectCognitive stateen_US
dc.subjectDynamical behavioren_US
dc.titleRhythms of the nervous system: mathematical themes and variationsen_US
dc.typeArticleen_US
dc.description.versionPublished versionen_US
pubs.elements-sourcearxiven_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
dc.identifier.orcid0000-0002-8568-8750 (Kopell, Nancy)


This item appears in the following Collection(s)

Show simple item record