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Delays in activity-based neural networks

Coombes, Stephen; Laing, Carlo

Authors

Carlo Laing



Abstract

In this paper, we study the effect of two distinct discrete delays on the dynamics of a Wilson-Cowan neural network. This activity-based model describes the dynamics of synaptically interacting excitatory and inhibitory neuronal populations. We discuss the interpretation of the delays in the language of neurobiology and show how they can contribute to the generation of network rhythms. First, we focus on the use of linear stability theory to show how to destabilize a fixed point, leading to the onset of oscillatory behaviour. Next, we show for the choice of a Heaviside nonlinearity for the firing rate that such emergent oscillations can be either synchronous or anti-synchronous, depending on whether inhibition or excitation dominates the network architecture. To probe the behaviour of smooth (sigmoidal) nonlinear firing rates, we use a mixture of numerical bifurcation analysis and direct simulations, and uncover parameter windows that support chaotic behaviour. Finally, we comment on the role of delays in the generation of bursting oscillations, and discuss natural extensions of the work in this paper. © 2009 The Royal Society.

Citation

Coombes, S., & Laing, C. (2009). Delays in activity-based neural networks. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 367(1891), 1117-1129. https://doi.org/10.1098/rsta.2008.0256

Journal Article Type Article
Publication Date Mar 28, 2009
Deposit Date Nov 19, 2008
Journal Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Electronic ISSN 1364-503X
Publisher Royal Society, The
Peer Reviewed Peer Reviewed
Volume 367
Issue 1891
Pages 1117-1129
DOI https://doi.org/10.1098/rsta.2008.0256
Keywords Wilson-Cowan networks,
multiple-delays,
phase-locking,
chaos
Public URL http://eprints.nottingham.ac.uk/id/eprint/1000
Publisher URL http://publishing.royalsociety.org/index.cfm?page=1570
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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