{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:17:38Z","timestamp":1758824258604,"version":"3.37.3"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2019,3]]},"abstract":"<jats:p> We propose an approach to study small limit cycle bifurcations on a center manifold in analytic or smooth systems depending on parameters. We then apply it to the investigation of limit cycle bifurcations in a model of calcium oscillations in the cilia of olfactory sensory neurons and show that it can have two limit cycles: a stable cycle appearing after a Bautin (generalized Hopf) bifurcation and an unstable cycle appearing after a subcritical Hopf bifurcation. <\/jats:p>","DOI":"10.1142\/s021812741950038x","type":"journal-article","created":{"date-parts":[[2019,3,28]],"date-time":"2019-03-28T23:24:34Z","timestamp":1553815474000},"page":"1950038","source":"Crossref","is-referenced-by-count":12,"title":["Limit Cycles in a Model of Olfactory Sensory Neurons"],"prefix":"10.1142","volume":"29","author":[{"given":"Yonghui","family":"Xia","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mateja","family":"Gra\u0161i\u010d","sequence":"additional","affiliation":[{"name":"Faculty of Natural Science and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia"},{"name":"Institute of Mathematics, Physics and Mechanics, SI-1000 Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6420-3232","authenticated-orcid":false,"given":"Wentao","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Science, Guilin University of Aerospace Technology, Guilin 541004, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valery G.","family":"Romanovski","sequence":"additional","affiliation":[{"name":"Faculty of Natural Science and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia"},{"name":"Faculty of Electrical Engineering and Computer Science, University of Maribor, SI-2000 Maribor, Slovenia"},{"name":"Center for Applied Mathematics and Theoretical Physics, SI-2000 Maribor, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,3,28]]},"reference":[{"key":"S021812741950038XBIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0064649"},{"key":"S021812741950038XBIB002","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1988-031-6"},{"volume-title":"Ordinary Differential Equations with Applications","year":"1999","author":"Chicone C.","key":"S021812741950038XBIB003"},{"key":"S021812741950038XBIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.02.050"},{"key":"S021812741950038XBIB006","doi-asserted-by":"publisher","DOI":"10.1137\/0520002"},{"key":"S021812741950038XBIB007","doi-asserted-by":"publisher","DOI":"10.1016\/0009-2509(87)80099-4"},{"volume-title":"Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields","year":"1990","author":"Guckenheimer J.","key":"S021812741950038XBIB008"},{"key":"S021812741950038XBIB009","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2421-9"},{"key":"S021812741950038XBIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s11786-007-0039-x"},{"key":"S021812741950038XBIB011","first-page":"108","volume":"219","author":"Niu W.","year":"2008","journal-title":"Appl. Math. Comput."},{"key":"S021812741950038XBIB012","first-page":"1297","volume":"28","author":"Pliss V. A.","year":"1964","journal-title":"Izv. Akad. Nauk SSSR, Ser. Mat."},{"key":"S021812741950038XBIB013","doi-asserted-by":"publisher","DOI":"10.1529\/biophysj.104.058545"},{"volume-title":"The Center and Cyclicity Problems: A Computational Algebra Approach","year":"2009","author":"Romanovski V. G.","key":"S021812741950038XBIB014"},{"key":"S021812741950038XBIB015","first-page":"153","volume":"23","author":"Shi S.","year":"1980","journal-title":"Sci. Sin. Ser. A"},{"key":"S021812741950038XBIB016","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1985-0783998-8"},{"key":"S021812741950038XBIB017","doi-asserted-by":"publisher","DOI":"10.1007\/s11786-008-0067-1"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812741950038X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T09:23:33Z","timestamp":1565083413000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812741950038X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3]]},"references-count":16,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2019,3,28]]},"published-print":{"date-parts":[[2019,3]]}},"alternative-id":["10.1142\/S021812741950038X"],"URL":"https:\/\/doi.org\/10.1142\/s021812741950038x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2019,3]]}}}