Codimension-3 bifurcation in the p53 regulatory network model. (English) Zbl 1472.34090
In this paper, the authors study the dynamical behaviors of the p53-Mdm2 model, and show that the model can undergo the saddle-node bifurcation, Hopf bifurcation, codimension-2 Bogdanov-Takens bifurcation, and codimension-3 Bogdanov-Takens bifurcation by rigorous mathematical analysis, and also explain the medical implications of these resluts.
Reviewer: Xiong Li (Beijing)
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 92D20 | Protein sequences, DNA sequences |
Keywords:
degenerate Bogdanov-Takens bifurcation; multi-stability; large oscillation; signaling pathway; DNA damageSoftware:
SingularityReferences:
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