Cascades of periodic solutions in a neural circuit with delays and slow-fast dynamics
dc.contributor.author | Ferrario, A | |
dc.contributor.author | Rankin, J | |
dc.date.accessioned | 2021-11-10T16:15:28Z | |
dc.date.issued | 2021-10-01 | |
dc.date.updated | 2021-11-10T16:03:04Z | |
dc.description.abstract | We analyse periodic solutions in a system of four delayed differential equations forced by periodic inputs representing two competing neural populations connected with fast mutual excitation and slow delayed inhibition. The combination of mechanisms generates a rich dynamical structure that we are able to characterize using slow-fast dissection and a binary classification of states. We previously proved the existence conditions of all possible states 1:1 locked to the inputs and applied this analysis to the tracking of the rhythms perceived when listening to alternating sequences of low and high tones. Here we extend this analysis using analytical and computational tools by proving the existence a set of n:1 periodically locked states and their location in parameter space. Firstly we examine cycle skipping states and find that they accumulate in an infinite cascade of period-incrementing bifurcations with increasing periods for decreasing values of the local input strength. Secondly we analyse periodic solutions that alternate between 1:1 locked states that repeat after an integer multiple of the input period (swapping states). We show that such states accumulate in similar bifurcation cascades with decreasing values of the lateral input strength. We report a parameter-dependent scaling constant for the ratio of widths of successive regions in the cascades, which generalises across cycle skipping and swapping states. The periodic states reported here - emergent behaviours in the model - can be linked to known phenomena in auditory perception that are beyond the original scope of the model’s design. | en_GB |
dc.description.sponsorship | Engineering and Physical Sciences Research Council | en_GB |
dc.description.sponsorship | Engineering and Physical Sciences Research Council | en_GB |
dc.identifier.citation | Vol. 7, article 716288 | en_GB |
dc.identifier.doi | https://doi.org/10.3389/fams.2021.716288 | |
dc.identifier.grantnumber | EP/R03124X/1 | en_GB |
dc.identifier.grantnumber | EP/T017856/1 | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/127768 | |
dc.identifier | ORCID: 0000-0002-8850-6027 (Rankin, J) | |
dc.language.iso | en | en_GB |
dc.publisher | Frontiers Media SA | en_GB |
dc.rights | Copyright © 2021 Ferrario and Rankin. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. | en_GB |
dc.subject | neural circuit | en_GB |
dc.subject | fast excitation | en_GB |
dc.subject | slow inhibition | en_GB |
dc.subject | periodic forcing | en_GB |
dc.subject | period incrementing bifurcation | en_GB |
dc.title | Cascades of periodic solutions in a neural circuit with delays and slow-fast dynamics | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2021-11-10T16:15:28Z | |
dc.description | This is the final version. Available from Frontiers Media via the DOI in this record. | en_GB |
dc.description | DATA AVAILABILITY STATEMENT: The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author. | en_GB |
dc.identifier.eissn | 2297-4687 | |
dc.identifier.journal | Frontiers in Applied Mathematics and Statistics | en_GB |
dc.relation.ispartof | Frontiers in Applied Mathematics and Statistics, 7 | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_GB |
dcterms.dateAccepted | 2021-08-31 | |
rioxxterms.version | VoR | en_GB |
rioxxterms.licenseref.startdate | 2021-10-01 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2021-11-10T16:11:34Z | |
refterms.versionFCD | VoR | |
refterms.dateFOA | 2021-11-10T16:15:37Z | |
refterms.panel | B | en_GB |
refterms.dateFirstOnline | 2021-10-01 |
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Except where otherwise noted, this item's licence is described as Copyright © 2021 Ferrario and Rankin. This is an open-access article distributed
under the terms of the Creative Commons Attribution License (CC BY). The use,
distribution or reproduction in other forums is permitted, provided the original
author(s) and the copyright owner(s) are credited and that the original publication
in this journal is cited, in accordance with accepted academic practice. No use,
distribution or reproduction is permitted which does not comply with these terms.