Date of Award
2007
Document Type
Dissertation
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Jirsa, Viktor K.
Abstract
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.
Extent
90 p.
Recommended Citation
Qubbaj, Murad R., "Neural field dynamics under vari ation of local and global connectivity and finite t ransmission speeds." (2007). Electronic Theses and Dissertations 2000 - 2009. 1313.
https://digitalcommons.fau.edu/etd_general_5/1313
Identifier
FA00000873
Comments
Includes bibliography.|Dissertation (Ph.D.)--Florida Atlantic University, 2007.|FAU Electronic Theses and Dissertations Collection|Charles E. Schmidt College of Science|Includes bibliography.