Journal article
Patterns and features of families of traveling waves in large-scale neuronal networks
SIAM journal on applied dynamical systems, Vol.6(1), pp.263-292
01/01/2007
DOI: 10.1137/06066638X
Abstract
We study traveling wave solutions of a system of integro-differential equations which describe the activity of large-scale networks of excitatory neurons on spatially extended domains. The independent variables are the activity level u of a population of excitatory neurons, which have long range connections, and a recovery variable v. We have found a critical value of the parameter beta (beta* > 0) that appears in the equation for v, at which the eigenvalues of the linearization of the system around the rest state (u, v) = (0, 0) change from real to complex. In contrast to previous studies which analyzed properties of traveling waves when the eigenvalues are real, we examine the range beta > beta*, where the eigenvalues are complex. In this case we show that there is a range of parameters over which families of wave fronts and 1-pulse and more general N-pulse waves can coexist as stable solutions. In two space dimensions our numerical experiments show how single-ring and multiring waves form in response to a Gaussian-shaped stimulus. With a spatially invariant coupling function, outwardly propagating waves can be periodically produced when a ring-shaped wave receives an appropriately timed perturbation. When the coupling is inhomogeneous the periodic production of waves eventually breaks down, and a stable one-armed rotating spiral wave emerges and fills the entire domain. It is noteworthy that all of these phenomena can be initiated at any point in the medium, that they are not driven by an underlying time dependent periodic pacemaker, and that they do not depend on the persistent or periodic presence of an external input.
Details
- Title: Subtitle
- Patterns and features of families of traveling waves in large-scale neuronal networks
- Creators
- William C. TroyVladimir Shusterman
- Resource Type
- Journal article
- Publication Details
- SIAM journal on applied dynamical systems, Vol.6(1), pp.263-292
- Publisher
- Siam Publications
- DOI
- 10.1137/06066638X
- ISSN
- 1536-0040
- eISSN
- 1536-0040
- Number of pages
- 30
- Language
- English
- Date published
- 01/01/2007
- Academic Unit
- Cardiovascular Medicine; Internal Medicine
- Record Identifier
- 9984360155602771
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