Codimension-3 Bifurcation in the p53 Regulatory Network Model

Author:

Jiang Cuicui12,Zhang Yongxin1,Wang Wendi1

Affiliation:

1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China

2. Department of Mathematics, College of Basic Medicine, Army Medical University, Chongqing 400038, P. R. China

Abstract

In this paper, a p53-Mdm2 mathematical model is analyzed to understand the biological implications of feedback loops in a p53 system. Results show that the model can undergo four types of codimension-3 Bogdanov–Takens bifurcations, including cusp, saddle, focus and elliptic. Specifically, we find new phenomena including the coexistence of four positive equilibria, two limit cycles, the coexistence of three stable states (two stable equilibria and one stable limit cycle, or three stable equilibria), a heteroclinic loop enclosing a smaller stable limit cycle and a larger stable limit cycle. These findings extend the understanding of the complex dynamics of the p53 system, and can provide some potential biological applications.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. STABILITY AND BIFURCATION ANALYSIS OF A SIMPLE DELAYED p53-Mdm2 GENE NETWORK MODEL WITH DIFFUSION;Journal of Biological Systems;2024-08-06

2. Modeling the p53-Mdm2 Dynamics Triggered by DNA Damage;Journal of Nonlinear Science;2024-03-31

3. Adaptive Weighted Neighbors Method for Sensitivity Analysis;Interdisciplinary Sciences: Computational Life Sciences;2022-04-15

4. Survival Reassessment at Tumor Recurrence in Soft Matter;Open Journal of Modelling and Simulation;2022

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