一类超越方程根的稳定性分析  

Stability analysis of the roots of a class transcendental equation

作　　者：马剑[1] 张春蕊[1] 

机构地区：[1]东北林业大学理学院,黑龙江哈尔滨150040

出　　处：《黑龙江大学自然科学学报》2006年第3期382-386,共5页Journal of Natural Science of Heilongjiang University

基　　金：中国博士后科学基金资助项目(2004036108);东北林业大学优秀创新项目

摘　　要：给出了一类超越方程根的稳定性的简单判别方法,利用Rouche定理和该方程根在复平面内的分布特点,分析了其稳定解的存在性,以及不同情形下是否会发生Hopf分支现象.同时,利用这些结论,在具体的应用中可以得到该类方程的纯虚根存在的充要条件、横截条件及Hopf分支的存在性,因此,具有重要的应用价值.A simple method to judge the stability of the roots of a class transcendental equation is given out. According the Routhe theorem and the characteristics of the solutions of the transcendental equation in the complex plane, the existence of the stable solutions is presented and the Hopf bifurcation for the different form of the class equation is discussed. Based on these conclusions, it expounds the existence of the pure imaginary roots, the transversal condition, and the existence of Hopf bifurcation for this class equation. So it is important significance in practical application.

关 键 词：超越方程 稳定性 时滞 HOPF分支 

分 类 号：O175.14[理学—数学]