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

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

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.

Suggested Citation

  • Marwan, Muhammad & Wang, Ning & Baig, Dur-e-Zehra & Li, Feng, 2025. "Practical computation of higher codimension Bogdanov–Takens bifurcations in energy supply–demand system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 238(C), pages 255-268.
    • Handle: RePEc:eee:matcom:v:238:y:2025:i:c:p:255-268
    DOI: 10.1016/j.matcom.2025.05.004
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    References listed on IDEAS

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