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  Phase response approaches to neural activity models with distributed delay

Winkler, M., Dumont, G., Schöll, E., Gutkin, B. (2022): Phase response approaches to neural activity models with distributed delay. - Biological Cybernetics, 116, 2, 191-203.
https://doi.org/10.1007/s00422-021-00910-9

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Winkler, Marius1, Author
Dumont, Grégory1, Author
Schöll, Eckehard2, Author              
Gutkin, Boris1, Author
Affiliations:
1External Organizations, ou_persistent22              
2Potsdam Institute for Climate Impact Research, Potsdam, ou_persistent13              

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 Abstract: In weakly coupled neural oscillator networks describing brain dynamics, the coupling delay is often distributed. We present a theoretical framework to calculate the phase response curve of distributed-delay induced limit cycles with infinite-dimensional phase space. Extending previous works, in which non-delayed or discrete-delay systems were investigated, we develop analytical results for phase response curves of oscillatory systems with distributed delay using Gaussian and log-normal delay distributions. We determine the scalar product and normalization condition for the linearized adjoint of the system required for the calculation of the phase response curve. As a paradigmatic example, we apply our technique to the Wilson–Cowan oscillator model of excitatory and inhibitory neuronal populations under the two delay distributions. We calculate and compare the phase response curves for the Gaussian and log-normal delay distributions. The phase response curves obtained from our adjoint calculations match those compiled by the direct perturbation method, thereby proving that the theory of weakly coupled oscillators can be applied successfully for distributed-delay-induced limit cycles. We further use the obtained phase response curves to derive phase interaction functions and determine the possible phase locked states of multiple inter-coupled populations to illuminate different synchronization scenarios. In numerical simulations, we show that the coupling delay distribution can impact the stability of the synchronization between inter-coupled gamma-oscillatory networks.

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Language(s): eng - English
 Dates: 2021-12-012021-12-022022-04
 Publication Status: Finally published
 Pages: 13
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1007/s00422-021-00910-9
PIKDOMAIN: RD4 - Complexity Science
Organisational keyword: RD4 - Complexity Science
Research topic keyword: Complex Networks
Research topic keyword: Nonlinear Dynamics
Model / method: Quantitative Methods
MDB-ID: No data to archive
 Degree: -

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Title: Biological Cybernetics
Source Genre: Journal, SCI, Scopus
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Pages: - Volume / Issue: 116 (2) Sequence Number: - Start / End Page: 191 - 203 Identifier: CoNE: https://publications.pik-potsdam.de/cone/journals/resource/biological-cybernetics
Publisher: Springer