Bifurcation analysis of the Topp model

V.A. Gaiko, A.E. Sterk, H.W. Broer

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Abstract

In this paper, we study the 3-dimensional Topp model for the dynamics
of diabetes. We show that for suitable parameter values an equilibrium of this model
bifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests that
near this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arise
through period doubling cascades of limit cycles.
Keywords Dynamics of diabetes · Topp model · Reduced planar quartic Topp
system · Singular point · Limit cycle · Hopf-saddle-node bifurcation · Period
doubling bifurcation · Shilnikov homoclinic orbit · Chaos
Original languageEnglish
Title of host publicationCurrent Trends in Analysis, its Applications and Computation
EditorsP. Cerejeiras, M. Reissig, I. Sabadini, J. Toft
Place of PublicationCham
PublisherSPRINGER BIRKHAUSER
Pages3-9
Number of pages7
ISBN (Electronic)978-3-030-87502-2
ISBN (Print)978-3-030-87501-5
DOIs
Publication statusPublished - 2022
EventCurrent Trends in Analysis, its Applications and Computation: The 12th ISAAC Congress, Aveiro, Portugal, 2019 - Aveiro, Portugal
Duration: 29-Jul-20192-Aug-2019

Conference

ConferenceCurrent Trends in Analysis, its Applications and Computation
Country/TerritoryPortugal
CityAveiro
Period29/07/201902/08/2019

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