Author(s)

S. Q. Ma

Department of Mathematics, China Agricultural University, Beijing, China.

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.

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

Ma, S. (2021) Bifurcation Analysis of the Regulatory Modules of the Mammalian M/G₁ Phase with Time Delay. International Journal of Modern Nonlinear Theory and Application, 10, 29-48. doi: 10.4236/ijmnta.2021.102003.