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
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 language | English |
|---|---|
| Title of host publication | Current Trends in Analysis, its Applications and Computation |
| Editors | P. Cerejeiras, M. Reissig, I. Sabadini, J. Toft |
| Place of Publication | Cham |
| Publisher | SPRINGER BIRKHAUSER |
| Pages | 3-9 |
| Number of pages | 7 |
| ISBN (Electronic) | 978-3-030-87502-2 |
| ISBN (Print) | 978-3-030-87501-5 |
| DOIs | |
| Publication status | Published - 2022 |
| Event | Current Trends in Analysis, its Applications and Computation: The 12th ISAAC Congress, Aveiro, Portugal, 2019 - Aveiro, Portugal Duration: 29-Jul-2019 → 2-Aug-2019 |
Conference
| Conference | Current Trends in Analysis, its Applications and Computation |
|---|---|
| Country/Territory | Portugal |
| City | Aveiro |
| Period | 29/07/2019 → 02/08/2019 |