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

Xin Pei, Jiang-Hong Hu, Mingtao Li, Yuchen Ding, Juping Zhang and Yongxin Zhang

Chaos, Solitons & Fractals, 2024, vol. 189, issue P1

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.

Keywords: Kim–Forger model; Circadian rhythms; Three limit cycles; Generalized Hopf bifurcation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011457

DOI: 10.1016/j.chaos.2024.115593

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