| 时滞基因调控网络的双稳定性和局部分岔 |
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| 引用本文： | 赖强,黄建宁.时滞基因调控网络的双稳定性和局部分岔[J].华中师范大学学报(自然科学版),2018,52(1):36-41. |
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| 作者姓名： | 赖强 黄建宁 |
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| 作者单位： | 1.华东交通大学 电气与自动化工程学院， 南昌 330013；2.南昌大学 科学技术学院 基础学科部， 南昌 330029 |
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| 摘 要： | 研究了含三个节点和两个反馈环的时滞基因调控网络的双稳定性和局部分岔.确定了该网络的正平衡点的个数.通过分析对应的特征方程，建立了网络双稳定性和Hopf分岔的存在性条件.研究结果显示，网络中正反馈环的存在会促使网络出现双稳定状态，而当网络有负反馈环且时滞达到某一临界值时，网络将产生Hopf分岔.数值仿真验证了理论结果的正确性.
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| 关 键 词： | 基因调控网络 时滞 双稳定性 局部分岔 |
| 收稿时间： | 2018-03-02 |
Bistability and local bifurcation of delayed gene regulatory network |
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| LAI Qiang,HUANG Jianning.Bistability and local bifurcation of delayed gene regulatory network[J].Journal of Central China Normal University(Natural Sciences),2018,52(1):36-41. |
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| Authors: | LAI Qiang HUANG Jianning |
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| Institution: | 1.School of Electrical and Automation Engineering， East China Jiaotong University， Nanchang 330013， China；2.Department of Basic Sciences， Nanchang University College of Science and Technology， Nanchang 330029， China |
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| Abstract: | This paper investigates the bistability and local bifurcation of delayed gene regulatory network with three nodes and two feedback loops. The existence of positive equilibrium point of the network is determined. By analyzing the corresponding characteristic equation， the existence conditions of the bistability and Hopf bifurcation the network have been obtained. It shows that the network may perform bistability when the network has positive feedback loop， and Hopf bifurcation will appear when the network has negative feedback loop and the time delay passes a critical value. Numerical simulations illustrate the correctness of our theoretical results. |
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| Keywords: | gene regulatory network time delay bistability local bifurcation |
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