Delays in activity-based neural networks

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
S Coombes, C R 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.

Associated Proceedings Papers

Dec 8, 2018·Sergei A. Plotnikov, Alexander L. Fradkov

References

Oct 20, 2010·International Journal of Molecular Sciences·Ildefonso Martínez de la Fuente
Nov 30, 2012·Journal of Mathematical Biology·S A van GilsS Visser
Jul 14, 2012·Neural Networks : the Official Journal of the International Neural Network Society·M U Akhmet, E Yılmaz
Apr 11, 2015·Journal of Mathematical Neuroscience·Ehsan NegahbaniJamie W Sleigh
Jan 8, 2016·Journal of Mathematical Neuroscience·Peter AshwinRachel Nicks
Jul 19, 2012·The European Journal of Neuroscience·Alex PavlidesRafal Bogacz
Jul 19, 2012·The European Journal of Neuroscience·Jaroslav Hlinka, S Coombes
Oct 1, 2012·IEEE Transactions on Neural Networks and Learning Systems·Yongli Song, Jian Xu
Jan 26, 2010·NeuroImage·S Coombes
Jan 21, 2015·Journal of Computational Neuroscience·Eugenio Urdapilleta, Inés Samengo
Apr 20, 2016·PLoS Computational Biology·Paola MalerbaMaxim Bazhenov
Jan 20, 2018·Physical Review. E·Jose M Esnaola-AcebesErnest Montbrió
Jun 12, 2018·International Journal of Neural Systems·Michael Caiola, Mark H Holmes
Feb 17, 2009·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Gabor Stepan
Dec 17, 2009·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Gábor OroszRichard M Murray
Apr 3, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jérémie Lefebvre, Theodore J Perkins
Nov 20, 2013·Biological cybernetics·Jesús Requena-CarriónJuan José Vinagre-Díaz
Oct 27, 2015·Neural Computation·Romain Veltz, Terrence J Sejnowski
Mar 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Lionel WeickerJan Danckaert

Citations

Jan 1, 1972·Biophysical Journal·H R Wilson, J D Cowan
Jan 1, 1989·Physical Review A: General Physics·C M Marcus, R M Westervelt
Nov 11, 1999·Proceedings of the National Academy of Sciences of the United States of America·D Golomb, G B Ermentrout
Nov 25, 2003·Neural Computation·C R Laing, André Longtin
Aug 2, 2005·Biological cybernetics·S Coombes
Aug 11, 2005·Physical Review Letters·Alex RoxinDavid Hansel
Jul 5, 2006·Network : Computation in Neural Systems·C R Laing, S Coombes
Feb 1, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S CoombesC R Laing

Related Concepts

Biological Neural Networks
Reaction Time
Neurons
Anatomic Bifurcation
Neural Network Simulation
Synaptic Potentials
Synapses
Neuronal
Neurobiology
Metabolic Inhibition

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