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https://doi.org/10.1073/pnas.0308265100

has been cited by the following article:

• TITLE: Bifurcation Analysis of the Regulatory Modules of the Mammalian M/G1 Phase with Time Delay

  AUTHORS: S. Q. Ma

  KEYWORDS: Cells Cycle, Time Delay, Hopf Bifurcation, Stability Switching, Normal Form

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.10 No.2, May 17, 2021

  ABSTRACT: G0/G1 “gaps” joint the S phase and M phase to form the cell cycle. The dynamics of enzyme reaction to drive the target protein production in M phase is analyzed mathematically. Time delay is introduced since the signal transmission need time in G0/G1 “gaps” phase. Hopf bifurcation of DDEs model is analyzed by applying geometrical analytical method. The instability oscillating periodic solutions arise as subcritical Hopf bifurcation occurs. The Hysteresis phenomena of the limit cycle are also observed underlying the saddle-node bifurcation of the limit cycle. Due to stability switching, interestingly, the bifurcating periodical solution dies out near the vicinity of Hopf lines. By Lyapunov-Schmidt reduction scheme, the normal form is computed on the center manifold. Finally, it is verified that the theory analytical results are in coincidence with the numerical simulation.