一个二维基因调控网络的稳定性和分岔分析  

Stability and Bifurcation Analysis of a Two-Dimensional Gene Regulatory Network

作　　者：杜鑫 毕远宏 刘全生[1] DU Xin;BI Yuanhong;LIU Quansheng(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;School of Statistics and Mathematics,Inner Mongolia University of Finance and Economics,Hohhot 010070,China;Inner Mongolia Key Laboratory of Economic Data Analysis and Mining,Hohhot 010070,China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]内蒙古财经大学统计与数学学院,呼和浩特010070 [3]内蒙古经济数据分析与挖掘重点实验室,呼和浩特010070

出　　处：《内蒙古大学学报（自然科学版）》2024年第4期350-358,共9页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金项目(12062017,12262025);内蒙古自然科学基金项目(2021ZD01);内蒙古高等学校创新团队发展计划项目(NMGIRT2208)。

摘　　要：基于动力系统理论分析一个二维基因调控网络的稳定性和分岔。首先,给出系统平衡点存在的条件并分析平衡点的稳定性。其次,分析该系统经历余维1的Hopf分岔、Saddle-node分岔以及余维2的Bogdanov-Takens分岔的条件。最后,用余维1、余维2分岔图和相图验证了理论结果的正确性。Stability and bifurcation analysis of a two-dimensional gene regulatory network is studied based on the dynamical systems theory.Firstly,the conditions for the existence of the equilibrium points are given,then stability of the equilibrium points is investigated.Secondly,the conditions for codimension-one Hopf bifurcation,Saddle-node bifurcation and codimension-two Bogdanov-Takens bifurcation are analyzed respectively.Finally,the correctness of the theoretical analysis is verified by the codimension-one bifurcation diagrams,codimension-two bifurcation diagram and phase diagrams.

关 键 词：基因调控网络 稳定性 分岔分析 

分 类 号：O193[理学—数学] O39[理学—基础数学]