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Bifurcations in brain dynamics.

Izhikevich, Eugene M.

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Bifurcations in brain dynamics.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Bifurcations in brain dynamics./
Author:	Izhikevich, Eugene M.
Description:	182 p.
Notes:	Adviser: F. C. Hoppensteadt.
Contained By:	Dissertation Abstracts International57-09B.
Subject:	Artificial Intelligence. -
Online resource:	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.
LDR:02128nam 2200349 a 45 001 929925
005 20110427
008 110427s1996 eng d
020 $a 0591134926
035 $a (UnM)AAI9706502
035 $a AAI9706502
040 $a UnM $c UnM
100 1 $a Izhikevich, Eugene M. $3 627841
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
650 4 $a Mathematics. $3 515831
690 $a 0317
690 $a 0405
690 $a 0544
690 $a 0790
690 $a 0800
710 2 0 $a Michigan State University. $3 676168
773 0 $t Dissertation Abstracts International $g 57-09B.
790 $a 0128
790 1 0 $a Hoppensteadt, F. C., $e advisor
791 $a Ph.D.
792 $a 1996
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9706502