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Neural field dynamics under vari ation of local and global connectivity and finite t ransmission speeds.

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Date Issued:
2007
Summary:
Spatially continuous networks with heterogeneous connections are ubiquitous in biological systems, in part icular neural systems. To understand the mutual effects of locally homogeneous and globally heterogeneous connectivity, the st ability of the steady state activity of a neural field as a fun ction of its connectivity is investigated. The variation of the connectivity is operationalized through manipulation of a heterogeneous two-point connection embedded into the otherwise homogeneous connectivity matrix and by variation of connectivity strength and transmission speed. A detailed discussion of the example of the real Ginzburg-Land au equation with an embedded two-point heterogeneous connection in addition to the homogeneous coupling due to the diffusion term is performed. The system is reduced to a set of delay differential equations and the stability di agrams as a function of the time delay and the local and global coupling strengths are computed. The major finding is that the stability of the heterogeneously connected elements with a well-defined velocity defines a lower bound for the stabil ity of the entire system . Diffusion and velocity dispersion always result in increased stability. Various other local architectures represented by exponentially decaying connectivity fun ctions are also discussed. The analysis shows that developmental changes such as the myelination of the cortical large-scale fib er system generally result in the stabilization of steady state activity via oscillatory instabilities independent of the local connectivity. Non-oscillatory (Turing) instabilities are shown to be independent of any influences of time delay.
Title: Neural field dynamics under vari ation of local and global connectivity and finite t ransmission speeds.
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Name(s): Qubbaj, Murad R.
Florida Atlantic University, Degree grantor
Jirsa, Viktor K., Thesis advisor
Charles E. Schmidt College of Science
Department of Physics
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2007
Date Issued: 2007
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 90 p.
Language(s): English
Summary: Spatially continuous networks with heterogeneous connections are ubiquitous in biological systems, in part icular neural systems. To understand the mutual effects of locally homogeneous and globally heterogeneous connectivity, the st ability of the steady state activity of a neural field as a fun ction of its connectivity is investigated. The variation of the connectivity is operationalized through manipulation of a heterogeneous two-point connection embedded into the otherwise homogeneous connectivity matrix and by variation of connectivity strength and transmission speed. A detailed discussion of the example of the real Ginzburg-Land au equation with an embedded two-point heterogeneous connection in addition to the homogeneous coupling due to the diffusion term is performed. The system is reduced to a set of delay differential equations and the stability di agrams as a function of the time delay and the local and global coupling strengths are computed. The major finding is that the stability of the heterogeneously connected elements with a well-defined velocity defines a lower bound for the stabil ity of the entire system . Diffusion and velocity dispersion always result in increased stability. Various other local architectures represented by exponentially decaying connectivity fun ctions are also discussed. The analysis shows that developmental changes such as the myelination of the cortical large-scale fib er system generally result in the stabilization of steady state activity via oscillatory instabilities independent of the local connectivity. Non-oscillatory (Turing) instabilities are shown to be independent of any influences of time delay.
Identifier: FA00000873 (IID)
Degree granted: Dissertation (Ph.D.)--Florida Atlantic University, 2007.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Charles E. Schmidt College of Science
Subject(s): Mathematical physics
Connections (Mathematics)
Superconductivity--Mathematics
Neural networks (Computer science)
Held by: Florida Atlantic University Libraries
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00000873
Sublocation: Digital Library
Use and Reproduction: Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.