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Three limit cycles in the Kim–Forger model of the mammalian circadian clock

Author

Listed:
  • Pei, Xin
  • Hu, Jiang-Hong
  • Li, Mingtao
  • Ding, Yuchen
  • Zhang, Juping
  • Zhang, Yongxin

Abstract

The Kim–Forger model is a fundamental mathematical model for understanding circadian rhythms. The limit cycles presented in the model is the dynamic mechanism of the periodic phenomena in the mammalian circadian clock. However, the full dynamics of the Kim–Forger model remain not completely understood. In this paper, we theoretically demonstrate that this model can undergo supercritical Hopf bifurcation, subcritical Hopf bifurcation, and generalized Hopf bifurcation of codimension two. Numerically, the system can exhibit 0, 1, 2, or 3 limit cycles. Our work complements and enriches the dynamical insights in the field of circadian rhythms.

Suggested Citation

  • Pei, Xin & Hu, Jiang-Hong & Li, Mingtao & Ding, Yuchen & Zhang, Juping & Zhang, Yongxin, 2024. "Three limit cycles in the Kim–Forger model of the mammalian circadian clock," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011457
    DOI: 10.1016/j.chaos.2024.115593
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