时滞基因调控网络的双稳定性和局部分岔  

Bistability and local bifurcation of delayed gene regulatory network

作　　者：赖强 黄建宁[2] 

机构地区：[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

出　　处：《华中师范大学学报（自然科学版）》2018年第1期36-41,共6页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(61603137);江西省自然科学基金项目(20171BAB212016)

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.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 charac- teristic 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.

关 键 词：基因调控网络 时滞 双稳定性 局部分岔 

分 类 号：O415[理学—理论物理]