文献类型：期刊文献

中文题名：时滞类Lorenz系统的Hopf分支

英文题名：Hopf Bifurcation of the Delayed Lorenz-like System

作者：李德奎[1];连玉平[1]

第一作者：李德奎

机构：[1]定西师范高等专科学校数学系

第一机构：甘肃中医药大学定西校区

年份：2014

期号：2

起止页码：1

中文期刊名：温州大学学报：自然科学版

基金：教育部科技研究重点项目(212180);甘肃省国际科技合作计划项目(1104WCGA195);定西师范高等专科学校青年项目(1329)

语种：中文

中文关键词：时滞类Lorenz系统;零平衡点;稳定性;Hopf分支

外文关键词：Delayed Lorenz-like System;Zero Equilibrium Point;Stability;Hopf Bifurcation

摘要：对类Lorenz系统的状态变量加上时滞得到一个泛函微分动力系统——时滞类Lorenz系统.首先给出了该系统仅存在零平衡点的条件,然后根据系统在零平衡点处的线性化系统对应的特征方程根的分布情况,给出了系统在零平衡点处稳定性和发生Hopf分支的条件,最后通过一些数值模拟验证了所得结论的正确性.
The delayed Lorenz-like system proposed in this paper is a system resulting from the addition of time delay to the state variables of Lorenz-like system. Firstly, the condition of Lorenz-like system only at zero equilibrium point was analyzed; secondly, according to the roots distribution of the associated characteristic equation corresponding to the linearized system of the system at the zero equilibrium point, the conditions were obtained for the asymptotic stability of the system and the emergence of Hopf bifurcation when the system stayed at zero equilibrium point;finally, some numerical simulations were given to verify the correctness of the conclusion.