Document Detail


On local bifurcations in neural field models with transmission delays.
MedLine Citation:
PMID:  23192328     Owner:  NLM     Status:  Publisher    
Abstract/OtherAbstract:
Neural field models with transmission delays may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay equations, among which DDE. In particular, it may be used advantageously for the investigation of stability and bifurcation of steady states. After introducing the neural field model in its basic functional analytic setting and discussing its spectral properties, we elaborate extensively an example and derive a characteristic equation. Under certain conditions the associated equilibrium may destabilise in a Hopf bifurcation. Furthermore, two Hopf curves may intersect in a double Hopf point in a two-dimensional parameter space. We provide general formulas for the corresponding critical normal form coefficients, evaluate these numerically and interpret the results.
Authors:
S A van Gils; S G Janssens; Yu A Kuznetsov; S Visser
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Publication Detail:
Type:  JOURNAL ARTICLE     Date:  2012-11-29
Journal Detail:
Title:  Journal of mathematical biology     Volume:  -     ISSN:  1432-1416     ISO Abbreviation:  J Math Biol     Publication Date:  2012 Nov 
Date Detail:
Created Date:  2012-11-29     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7502105     Medline TA:  J Math Biol     Country:  -    
Other Details:
Languages:  ENG     Pagination:  -     Citation Subset:  -    
Affiliation:
Department of Applied Mathematics, University of Twente, PO Box 217, 7500 AE, Enschede, The Netherlands, S.A.vanGils@utwente.nl.
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