Hopf Bifurcation Analysis of the Halvorsen System
Year: 2025
Type: article
Abstract: This paper investigates local bifurcations in the Halvorsen system, focusing specifically on transcritical and Hopf bifurcations. The behavior of equilibrium points during bifurcations is studied using Sotomayor's theorem for transcritical bifurcation and normal form theory, which is based on Hassard's formulas, for Hopf bifurcation. When the bifurcation parameter exceeds a critical value, a Hopf bifurcation emerges. By applying normal form theory, we establish the conditions under which a Hopf bifurcation occurs. Furthermore, we discuss the direction of the Hopf bifurcation and the stability of the resulting periodic orbits. Finally, numerical simulations are provided to support the theoretical findings.
Authors: Kardo Baiz Othman, Adnan Ali Jalal
Institution: Salahaddin University-Erbil
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7117664323