Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing

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dc.citation.issue2266
dc.citation.volume478
dc.contributor.authorLaing CR
dc.contributor.authorKrauskopf B
dc.date.accessioned2023-11-15T01:47:56Z
dc.date.accessioned2023-11-20T01:38:04Z
dc.date.available2022-10-26
dc.date.available2023-11-15T01:47:56Z
dc.date.available2023-11-20T01:38:04Z
dc.date.issued2022-10-26
dc.description.abstractWe consider a single theta neuron with delayed self-feedback in the form of a Dirac delta function in time. Because the dynamics of a theta neuron on its own can be solved explicitly—it is either excitable or shows self-pulsations—we are able to derive algebraic expressions for the existence and stability of the periodic solutions that arise in the presence of feedback. These periodic solutions are characterized by one or more equally spaced pulses per delay interval, and there is an increasing amount of multistability with increasing delay time. We present a complete description of where these self-sustained oscillations can be found in parameter space; in particular, we derive explicit expressions for the loci of their saddle-node bifurcations. We conclude that the theta neuron with delayed self-feedback emerges as a prototypical model: it provides an analytical basis for understanding pulsating dynamics observed in other excitable systems subject to delayed self-coupling.
dc.description.confidentialfalse
dc.edition.editionOctober 2022
dc.identifier.citationLaing CR, Krauskopf B. (2022). Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 478. 2266.
dc.identifier.doi10.1098/rspa.2022.0292
dc.identifier.eissn1471-2946
dc.identifier.elements-typejournal-article
dc.identifier.issn1364-5021
dc.identifier.number20220292
dc.identifier.urihttps://mro.massey.ac.nz/handle/10179/69153
dc.languageEnglish
dc.publisherThe Royal Society Publishing
dc.publisher.urihttps://royalsocietypublishing.org/doi/10.1098/rspa.2022.0292#d9414020e1
dc.relation.isPartOfProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
dc.rights(c) 2022 The Author/s
dc.rightsCC BY 4.0
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectneuron dynamics
dc.subjectself-pulsations
dc.subjectdelay differential equations
dc.subjectbifurcation analysis
dc.titleTheta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing
dc.typeJournal article
pubs.elements-id457469
pubs.organisational-groupOther
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