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Bifurcations in brain dynamics.

Izhikevich, Eugene M.

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Bifurcations in brain dynamics.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Bifurcations in brain dynamics./
作者:	Izhikevich, Eugene M.
面頁冊數:	182 p.
附註:	Adviser: F. C. Hoppensteadt.
Contained By:	Dissertation Abstracts International57-09B.
標題:	Artificial Intelligence. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9706502
ISBN:	0591134926

Bifurcations in brain dynamics.
Izhikevich, Eugene M.

Bifurcations in brain dynamics. - 182 p.

Adviser: F. C. Hoppensteadt.

Thesis (Ph.D.)--Michigan State University, 1996.

A part of this dissertation (Chapters 2 and 7) received the SIAM Student Paper Prize in applied mathematics for 1995.

ISBN: 0591134926Subjects--Topical Terms:

769149
Artificial Intelligence.

Bifurcations in brain dynamics.
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245 1 0 $a Bifurcations in brain dynamics.
300 $a 182 p.
500 $a Adviser: F. C. Hoppensteadt.
500 $a Source: Dissertation Abstracts International, Volume: 57-09, Section: B, page: 5891.
502 $a Thesis (Ph.D.)--Michigan State University, 1996.
520 $a A part of this dissertation (Chapters 2 and 7) received the SIAM Student Paper Prize in applied mathematics for 1995.
520 $a Mathematical models of the brain are studied with the assumption that the connections between neurons are weak. This leads to weakly connected systems, which are called Weakly Connected Neural Networks (WCNNs). Local dynamics of the WCNNs is studied using bifurcation theory.
520 $a First it is proved that the WCNNs could have interesting local dynamics with possible applications to neurocomputers only near bifurcations. Then it is shown that near the bifurcations the WCNNs can be significantly simplified and reduced to canonical models.
520 $a Derivation and analysis of the canonical models for multiple (quasi-static) saddle-node, pitchfork and Andronov-Hopf bifurcations and multiple cusp singularities is presented. Mathematical analysis of the canonical models suggests a new neural network paradigm--non-hyperbolic neural networks. It also sheds some light on possible synaptic organizations of the brain. In particular, it reveals the relationship between synaptic architectures (anatomy) and dynamical properties (function) of networks of neural oscillators.
590 $a School code: 0128.
650 4 $a Artificial Intelligence. $3 769149
650 4 $a Biology, Neuroscience. $3 1017680
650 4 $a Engineering, Electronics and Electrical. $3 626636
650 4 $a Engineering, System Science. $3 1018128
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