Mathematical analysis of a generalised p53-Mdm2 protein gene expression model

作者：

Highlights：

• Generalization of the p53-Mdm2 protein gene expression model is presented.

• Existence of invariant set, uniqueness and global existence of solutions are proved.

• Conditions guaranteeing the existence of oscillatory solutions are given.

• Stability of the periodic solutions born due to the Hopf bifurcation is studied.

• Influence of the Hill coefficient in the Mdm2 mRNA production function is discussed.

摘要

•Generalization of the p53-Mdm2 protein gene expression model is presented.•Existence of invariant set, uniqueness and global existence of solutions are proved.•Conditions guaranteeing the existence of oscillatory solutions are given.•Stability of the periodic solutions born due to the Hopf bifurcation is studied.•Influence of the Hill coefficient in the Mdm2 mRNA production function is discussed.

论文关键词：Delay differential equations,Stability analysis,Hopf bifurcation,p53 protein

论文评审过程：Received 28 January 2017, Revised 4 June 2017, Accepted 12 January 2018, Available online 6 February 2018, Version of Record 6 February 2018.

论文官网地址：https://doi.org/10.1016/j.amc.2018.01.014