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Synchrony-induced modes of oscillation of a neural field model

Esnaola-Acebes, Jose M.; Roxin, Alex; Avitabile, Daniele; Montbrio, Ernest

Authors

Jose M. Esnaola-Acebes

Alex Roxin

Daniele Avitabile

Ernest Montbrio



Abstract

We investigate the modes of oscillation of heterogeneous ring-networks of quadratic integrate-and-fire (QIF) neurons with non-local, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient standing waves with a specific temporal frequency, analogous to those in a tense string. In the neuronal network, the equilibrium corresponds to a spatially homogeneous, asynchronous state. Perturbations of this state excite the network’s oscillatory modes, which reflect the interplay of episodes of synchronous spiking with the excitatory-inhibitory spatial interactions. In the thermodynamic limit, an exact low-dimensional neural field model (QIF-NFM) describing the macroscopic dynamics of the network is derived. This allows us to obtain formulas for the Turing eigenvalues of the spatially-homogeneous state, and hence to obtain its stability boundary. We find that the frequency of each Turing mode depends on the corresponding Fourier coefficient of the synaptic pattern of connectivity. The decay rate instead, is identical for all oscillation modes as a consequence of the heterogeneity-induced desynchronization of the neurons. Finally, we numerically compute the spectrum of spatially-inhomogeneous solutions branching from the Turing bifurcation, showing that similar oscillatory modes operate in neural bump states, and are maintained away from onset.

Journal Article Type Article
Publication Date Nov 13, 2017
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 1550-2376
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 96
Issue 5
Article Number 052407
APA6 Citation Esnaola-Acebes, J. M., Roxin, A., Avitabile, D., & Montbrio, E. (2017). Synchrony-induced modes of oscillation of a neural field model. Physical Review E, 96(5), doi:10.1103/PhysRevE.96.052407
DOI https://doi.org/10.1103/PhysRevE.96.052407
Publisher URL https://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.052407
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information ©2017 American Physical Society

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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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