Practical computation of higher codimension Bogdanov–Takens bifurcations in energy supply–demand system

Muhammad Marwan, Ning Wang, Dur-e-Zehra Baig and Feng Li

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 238, issue C, 255-268

Abstract: The analysis of energy crises is significant research topic in both theory and engineering. In the current paper, a nonlinear, real-life based model of energy resources transportation between two cities is considered to study codimension-1, codimension-2, and codimension-3 bifurcations using the first Lyapunov coefficient and generalized eigenvectors. The first Lyapunov coefficient (LC) provides sufficient information about the type of Hopf bifurcation and the emergence of a Bautin bifurcation at the critical points. Moreover, it is proved that there exists codimension-two Bogdanov–Takens (BT) bifurcation exhibiting Hopf, saddle–node and homoclinic local bifurcation curves at their specific parameters. Additionally, under certain conditions, the normal form of the codimension-three Bogdanov–Takens bifurcation is derived and analyzed.

Keywords: Chaotic system; Hopf bifurcation; First Lyapunov coefficient; Bogdanov–Takens bifurcation; Generalized eigenvectors; Codimension bifurcation; MATLAB (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:238:y:2025:i:c:p:255-268

DOI: 10.1016/j.matcom.2025.05.004

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