Bifurcation analysis of a two-dimensional p53 gene regulatory network without and with time delay

被引:1
|
作者
Du, Xin [1 ]
Liu, Quansheng [1 ]
Bi, Yuanhong [2 ,3 ]
机构
[1] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China
[2] Inner Mongolia Univ Finance & Econ, Sch Stat & Math, Hohhot 010070, Peoples R China
[3] Inner Mongolia Key Lab Econ Data Anal & Min, Hohhot 010070, Peoples R China
来源
ELECTRONIC RESEARCH ARCHIVE | 2023年 / 32卷 / 01期
基金
中国国家自然科学基金;
关键词
stability; saddle-node bifurcation; Hopf bifurcation; Bogdanov-Takens bifurcation; time delay; DYNAMICS; MODEL; STABILITY; BEHAVIOR;
D O I
10.3934/era.2024014
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, the stability and bifurcation of a two-dimensional p53 gene regulatory net-work without and with time delay are taken into account by rigorous theoretical analyses and numerical simulations. In the absence of time delay, the existence and local stability of the positive equilibrium are considered through the Descartes' rule of signs, the determinant and trace of the Jacobian matrix, respectively. Then, the conditions for the occurrence of codimension-1 saddle-node and Hopf bifurca-tion are obtained with the help of Sotomayor's theorem and the Hopf bifurcation theorem, respectively, and the stability of the limit cycle induced by hopf bifurcation is analyzed through the calculation of the first Lyapunov number. Furthermore, codimension-2 Bogdanov-Takens bifurcation is investigated by calculating a universal unfolding near the cusp. In the presence of time delay, we prove that time delay can destabilize a stable equilibrium. All theoretical analyses are supported by numerical sim-ulations. These results will expand our understanding of the complex dynamics of p53 and provide several potential biological applications.
引用
收藏
页码:293 / 316
页数:24
相关论文
共 50 条
  • [41] Dynamics of p53 regulatory network in DNA damage response
    Gao, Chunyan
    Chen, Fangqi
    APPLIED MATHEMATICAL MODELLING, 2020, 88 : 701 - 714
  • [42] Mechanisms of regulatory diversity within the p53 transcriptional network
    Espinosa, J. M.
    ONCOGENE, 2008, 27 (29) : 4013 - 4023
  • [43] GENOME-WIDE ANALYSIS OF THE p53 GENE REGULATORY NETWORKS IN THE DEVELOPING KIDNEY
    Li, Y.
    McLaughlin, N. J.
    Saifudeen, Z. R.
    Bachvarov, D.
    Dipp, S.
    El-Dahr, S. S.
    JOURNAL OF INVESTIGATIVE MEDICINE, 2011, 59 (02) : 463 - 463
  • [44] Network Effect of Wt-mutant p53 Interactions and Implications on p53 Gene Therapy
    Ji, Xiaona
    Ma, Lijie
    Huang, Qiang
    Li, Zijuan
    Zhao, Jing
    Huang, Weixue
    Ma, Buyong
    Yu, Long
    CURRENT PHARMACEUTICAL DESIGN, 2014, 20 (08) : 1259 - 1267
  • [45] Bifurcation analysis of fractional-order gene regulatory system with delay
    Zhang Zhe
    Zhang Jing
    He Guangyu
    Li Mingzhu
    Liu Feng
    2018 13TH WORLD CONGRESS ON INTELLIGENT CONTROL AND AUTOMATION (WCICA), 2018, : 1353 - 1359
  • [46] Analysis of p53 gene mutations in parapsoriasis
    Baskan, E. B.
    Tunca, B.
    Cecener, G.
    Tunali, S.
    Egeli, Ue
    Saricaoglu, H.
    Adim, S. B.
    JOURNAL OF THE EUROPEAN ACADEMY OF DERMATOLOGY AND VENEREOLOGY, 2006, 20 (07) : 882 - 883
  • [47] Dynamic behavior of P53-Mdm2-Wip1 gene regulatory network under the influence of time delay and noise
    Luo, LanJiang
    Liu, Haihong
    Yan, Fang
    MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2023, 20 (02) : 2321 - 2347
  • [48] p53: a two-faced cancer gene
    Kastan, Michael B.
    Berkovich, Elijahu
    NATURE CELL BIOLOGY, 2007, 9 (05) : 489 - 491
  • [49] p53: a two-faced cancer gene
    Michael B. Kastan
    Elijahu Berkovich
    Nature Cell Biology, 2007, 9 : 489 - 491
  • [50] Oscillatory Dynamics of P53 Network With Time Delays
    Wang, Conghua
    Yan, Fang
    Zhang, Yuan
    Liu, Haihong
    Zhang, Linghai
    COMBINATORIAL CHEMISTRY & HIGH THROUGHPUT SCREENING, 2018, 21 (06) : 411 - 419