{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:28:41Z","timestamp":1747189721310,"version":"3.40.5"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"15","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,12,15]]},"abstract":"<jats:p> Based on the Hodgkin\u2013Huxley and Hindmarsh\u2013Rose models, this paper proposes a geometric phenomenological model of bursting neuron in its simplest form, describing the dynamic motion on a mug-shaped branched manifold, which is a cylinder tied to a ribbon. Rigorous mathematical analysis is performed on the nature of the bursting neuron solutions: the number of spikes in a burst, the periodicity or chaoticity of the bursts, etc. The model is then generalized to obtain mixing burst of any number of spikes. Finally, an example is presented to verify the theoretical results. <\/jats:p>","DOI":"10.1142\/s021812742030044x","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T10:44:48Z","timestamp":1607597088000},"page":"2030044","source":"Crossref","is-referenced-by-count":0,"title":["Geometrical Model of Spiking and Bursting Neuron on a Mug-Shaped Branched Manifold"],"prefix":"10.1142","volume":"30","author":[{"given":"Mohamed","family":"Gheouali","sequence":"first","affiliation":[{"name":"University of Sciences and Technologies, Houari Boumediene (USTHB), Mathematical Faculty, 16111 El Alia, Bab Ezzouar, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tounsia","family":"Benzekri","sequence":"additional","affiliation":[{"name":"University of Sciences and Technologies, Houari Boumediene (USTHB), Mathematical Faculty, 16111 El Alia, Bab Ezzouar, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0451-4255","authenticated-orcid":false,"given":"Ren\u00e9","family":"Lozi","sequence":"additional","affiliation":[{"name":"Universit\u00e9 C\u00f4te d\u2019Azur, CNRS, Laboratoire J. 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