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Titolo:
Bifurcations in a planar system of differential delay equations modeling neural activity
Autore:
Giannakopoulos, F; Zapp, A;
Indirizzi:
Fraunhofer Inst Autonomous Intelligent Syst, D-53754 St Augustin, Germany Fraunhofer Inst Autonomous Intelligent Syst St Augustin Germany D-53754 Univ Cologne, Inst Math, D-50931 Cologne, Germany Univ Cologne Cologne Germany D-50931 Inst Math, D-50931 Cologne, Germany
Titolo Testata:
PHYSICA D
fascicolo: 3-4, volume: 159, anno: 2001,
pagine: 215 - 232
SICI:
0167-2789(20011115)159:3-4<215:BIAPSO>2.0.ZU;2-8
Fonte:
ISI
Lingua:
ENG
Soggetto:
PERIODIC-SOLUTIONS; NETWORK MODEL; 2 DELAYS; STABILITY;
Keywords:
neural activity; nonlinear delay differential equations; saddle-node bifurcation; Hopf bifurcation; Bogdanov-Takens bifurcation;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
28
Recensione:
Indirizzi per estratti:
Indirizzo: Giannakopoulos, F Fraunhofer Inst Autonomous Intelligent Syst, Schloss Birlinghoven, D-53754St Augustin, Germany Fraunhofer Inst Autonomous Intelligent Syst Schloss Birlinghoven St Augustin Germany D-53754
Citazione:
F. Giannakopoulos e A. Zapp, "Bifurcations in a planar system of differential delay equations modeling neural activity", PHYSICA D, 159(3-4), 2001, pp. 215-232

Abstract

A planar system of differential delay equations modeling neural activity is investigated. The stationary points and their saddle-node bifurcations are estimated. By an analysis of the associated characteristic equation, Hopfbifurcations are demonstrated. At the intersection points of the saddle-node and Hopf bifurcation curves in an appropriate parameter plane, the existence of Bogdanov-Takens singularities is shown. The properties of the Bogdanov-Takens singularities are studied by applying the center manifold and normal form theory. A numerical example illustrates the obtained results. (C)2001 Elsevier Science B.V. All rights reserved.

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Documento generato il 21/10/20 alle ore 11:17:29