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On the stability of singular Hopf bifurcation and its application

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  • Li, Jun
  • Li, Shimin
  • Ma, Mingju
  • Wu, Kuilin

Abstract

Krupa et al. (2001) proposed a method to determine the stability of limit cycles bifurcated from singular Hopf bifurcations in slow-fast systems. However, this method is invalid for the degenerate case (i.e., A=0). This paper deals with this degenerate case. Employing the blow-up method and normal form theory, we derive an approximate expression for the first Lyapunov coefficient when A=0. As an application, we investigate the singular Hopf bifurcation of a predator–prey model with Allee effects and validate the applicability of our result.

Suggested Citation

  • Li, Jun & Li, Shimin & Ma, Mingju & Wu, Kuilin, 2026. "On the stability of singular Hopf bifurcation and its application," Chaos, Solitons & Fractals, Elsevier, vol. 208(P3).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p3:s0960077926004418
    DOI: 10.1016/j.chaos.2026.118300
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