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_/ 流体力学セミナー ２００６ No. １２
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_/ 日 時 : ０６年 １１月 ２０日 (月) １５：００〜１６：３０
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_/ 場 所 : 京大数理研 ００９号室
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_/ 講 師： Dr. Lennaert van Veen
_/ La Trobe University, Melbourne, Australia
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_/ 題 目： The Shilnikov-saddle node bifurcation and robust chaos
_/ in the brain
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_/ 内 容 :
_/ The study of the human brain as a dynamical system is
_/ complicated enormously by the multitude of open questions
_/ on modeling as well as the correlation between the signals
_/ in the brain and the process of cognition. Many have tried
_/ to model the brain as a network of coupled units, each
_/ modeling some aspect of the functioning of neurons. However,
_/ the number and density of the neurons suggest that
_/ local-average modeling is a better approach. In this approach
_/ an system of partial differential equations is derived for
_/ the spatio-temporal variation of brain signals. In collaboration
_/ with David Liley of Swinburne University, Melbourne, I have
_/ studied the dynamics of a local average model for electro-cortical
_/ activity. Surprisingly, we found that chaotic behaviour in this
_/ model is quite common. The route to chaos followed is called the
_/ Shilnikov-saddle node bifurcation and has never been found in a
_/ physical application before. The fact that this particular model has
_/ been proven to model many aspects of the human electroencephalogram
_/ (EEG) correctly (currently clinical trials are conducted with an EEG
_/ reader based on this model) this has interesting implications for
_/ brain functioning.
_/ The presentation is based on “Chaos in the electroencephalogram
_/ via Shilnikov’s saddle-node bifurcation”, Phys.Rev.Lett.,
_/ to appear in November 2006
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