Bifurcation analysis of a two-dimensional p53 gene regulatory network without and with time delay
被引:1
|
作者:
Du, Xin
论文数: 0引用数: 0
h-index: 0
机构:
Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R ChinaInner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China
Du, Xin
[1
]
Liu, Quansheng
论文数: 0引用数: 0
h-index: 0
机构:
Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R ChinaInner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China
Liu, Quansheng
[1
]
Bi, Yuanhong
论文数: 0引用数: 0
h-index: 0
机构:
Inner Mongolia Univ Finance & Econ, Sch Stat & Math, Hohhot 010070, Peoples R China
Inner Mongolia Key Lab Econ Data Anal & Min, Hohhot 010070, Peoples R ChinaInner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China
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
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.
机构:
Yunnan Normal Univ, Dept Math, Kunming 650500, Peoples R China
Univ Yunnan, Key Lab Complex Syst Modeling & Applicat, Kunming 650500, Peoples R ChinaYunnan Normal Univ, Dept Math, Kunming 650500, Peoples R China
Luo, LanJiang
Liu, Haihong
论文数: 0引用数: 0
h-index: 0
机构:
Yunnan Normal Univ, Dept Math, Kunming 650500, Peoples R China
Univ Yunnan, Key Lab Complex Syst Modeling & Applicat, Kunming 650500, Peoples R ChinaYunnan Normal Univ, Dept Math, Kunming 650500, Peoples R China
Liu, Haihong
Yan, Fang
论文数: 0引用数: 0
h-index: 0
机构:
Yunnan Normal Univ, Dept Math, Kunming 650500, Peoples R China
Univ Yunnan, Key Lab Complex Syst Modeling & Applicat, Kunming 650500, Peoples R ChinaYunnan Normal Univ, Dept Math, Kunming 650500, Peoples R China
机构:
Yunnan Normal Univ, Coll Math, Kunming 650500, Yunnan, Peoples R ChinaYunnan Normal Univ, Coll Math, Kunming 650500, Yunnan, Peoples R China
Wang, Conghua
Yan, Fang
论文数: 0引用数: 0
h-index: 0
机构:
Yunnan Normal Univ, Coll Math, Kunming 650500, Yunnan, Peoples R ChinaYunnan Normal Univ, Coll Math, Kunming 650500, Yunnan, Peoples R China
Yan, Fang
Zhang, Yuan
论文数: 0引用数: 0
h-index: 0
机构:
Shanghai Univ, Shanghai Inst Appl Math & Mech, Shanghai 200072, Peoples R ChinaYunnan Normal Univ, Coll Math, Kunming 650500, Yunnan, Peoples R China
Zhang, Yuan
Liu, Haihong
论文数: 0引用数: 0
h-index: 0
机构:
Yunnan Normal Univ, Coll Math, Kunming 650500, Yunnan, Peoples R ChinaYunnan Normal Univ, Coll Math, Kunming 650500, Yunnan, Peoples R China
Liu, Haihong
Zhang, Linghai
论文数: 0引用数: 0
h-index: 0
机构:
Lehigh Univ, Dept Math, Bethlehem, PA 18015 USAYunnan Normal Univ, Coll Math, Kunming 650500, Yunnan, Peoples R China