{"title":"Hopf bifurcation analysis of the fast subsystem of a polynomial phantom burster model","authors":"I. M. Bulai, M. G. Pedersen","doi":"10.14658/PUPJ-DRNA-2018-3-2","DOIUrl":null,"url":null,"abstract":"Phantom bursters were introduced to explain bursting electrical activity in β -cells with different periods. We study a polynomial version of the phantom bursting model. In particular we analyse the fast subsystem, where the slowest variable is assumed constant. We find the equilibrium points of the fast subsystem and analyse their stability. Furthermore an analytical analysis of the existence of Hopf bifurcation points and the stability of the resulting periodics is performed by studying the sign of the first Lyapunov coefficient.","PeriodicalId":51943,"journal":{"name":"Dolomites Research Notes on Approximation","volume":"11 1","pages":"3-10"},"PeriodicalIF":0.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dolomites Research Notes on Approximation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14658/PUPJ-DRNA-2018-3-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
Phantom bursters were introduced to explain bursting electrical activity in β -cells with different periods. We study a polynomial version of the phantom bursting model. In particular we analyse the fast subsystem, where the slowest variable is assumed constant. We find the equilibrium points of the fast subsystem and analyse their stability. Furthermore an analytical analysis of the existence of Hopf bifurcation points and the stability of the resulting periodics is performed by studying the sign of the first Lyapunov coefficient.
期刊介绍：
Dolomites Research Notes on Approximation is an open access journal that publishes peer-reviewed papers. It also publishes lecture notes and slides of the tutorials presented at the annual Dolomites Research Weeks and Workshops, which have been organized regularly since 2006 by the Padova-Verona Research Group on Constructive Approximation and Applications (CAA) in Alba di Canazei (Trento, Italy). The journal publishes, on invitation, survey papers and summaries of Ph.D. theses on approximation theory, algorithms, and applications.
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