Hopf bifurcation analysis of the fast subsystem of a polynomial phantom burster model

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.

Bulai I. M., Gram Pedersen M. (2018) "Hopf bifurcation analysis of the fast subsystem of a polynomial phantom burster model " Dolomites Research Notes on Approximation, 11(3), 3-10. DOI: 10.14658/PUPJ-DRNA-2018-3-2  
Year of Publication
2018
Journal
Dolomites Research Notes on Approximation
Volume
11
Issue Number
3
Start Page
3
Last Page
10
Date Published
11/2018
ISSN Number
2035-6803
Serial Article Number
2
DOI
10.14658/PUPJ-DRNA-2018-3-2
Issue
Section
SpecialIssue3