| 延迟遗传调控网络稳定性及分支 |
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| 引用本文： | 王晶囡,蒋卫华.延迟遗传调控网络稳定性及分支[J].生物数学学报,2008,23(4):647-655. |
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| 作者姓名： | 王晶囡 蒋卫华 |
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| 作者单位： | 1. 哈尔滨理工大学,应用数学系,黑龙江,哈尔滨,150080;哈尔滨工业大学,理学院数学系,黑龙江,哈尔滨,150001
2. 哈尔滨工业大学,理学院数学系,黑龙江,哈尔滨,150001 |
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| 基金项目： | 黑龙江省自然科学基金，哈尔滨工业大学理学研究基金 |
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| 摘 要： | 本文主要研究了延迟遗传调控网络的局部稳定性和该网络的Hopf分支存在条件．延迟遗传调控网络是无穷维系统，此类系统在平衡点线性化后的特征方程为超越方程。通过对此超越方程进行研究，得到了系统系数不同时的系统稳定的条件及相关结论，又进一步说明了此系统的Hopf分支存在条件．最后，举一个例子进行了数值仿真验证了所得到的结论．
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| 关 键 词： | 遗传调控网络 稳定性 延迟 Hopf分支 |
Stability and Bifurcation of Genetic Regulatory Networks with Time Delays |
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| WANG Jing-nan,JIANG Wei-hua.Stability and Bifurcation of Genetic Regulatory Networks with Time Delays[J].Journal of Biomathematics,2008,23(4):647-655. |
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| Authors: | WANG Jing-nan JIANG Wei-hua |
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| Institution: | WANG Jing-nan, JIANG Wei-hua (1 Department of applied mathematics, Harbin University of science and technology, Harbin Heilongjiang 150080 china;2 Department of mathematics, science school, Harbin Institute of Technology, Harbin Heilongjiang 150001 china) |
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| Abstract: | paper deals with the local stability and Hopf bifurcation of Genetic regulatory networks with time delays,the network is an infinite dimensional system and its characteristic equation of corresponding linearization system at equilibrium is a transcendental equation.We study this equation and obtain some stability conditions with different coefficients of this system as well as some relevant results.Furthermore,we present some existence conditions of Hopf bifurcation.Finally,An example is given and numerical simulations are performed to illustrate obtained results. |
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| Keywords: | Genetic regulatory networks Stability Delay Hopf bifurcation |
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