具时滞人机系统的稳定性与分支分析

数学季刊 ›› 2012, Vol. 27 ›› Issue (2): 196-203.

具时滞人机系统的稳定性与分支分析

Department of Mathematics and Computer Science, Ningxia Teacher’s University

收稿日期:2010-05-10 出版日期:2012-06-30 发布日期:2023-03-28
作者简介:YANG Ji-hua(1983-), male, native of Zhoukou, Henan, a lecturer of Ningxia Teacher’s University, M.S.D., engages in qualitative theory of ordinary diﬀerential equation.
基金资助:
Supported by the Natural Science Foundation of Ningxia(NZ09204)； Supported by the Youth Foundation of Ningxia Teacher’s University(QN2010002)

Stability and Bifurcation Analysis of Man-machine System with Time Delay

Department of Mathematics and Computer Science, Ningxia Teacher’s University

Received:2010-05-10 Online:2012-06-30 Published:2023-03-28
About author:YANG Ji-hua(1983-), male, native of Zhoukou, Henan, a lecturer of Ningxia Teacher’s University, M.S.D., engages in qualitative theory of ordinary diﬀerential equation.
Supported by:
Supported by the Natural Science Foundation of Ningxia(NZ09204)； Supported by the Youth Foundation of Ningxia Teacher’s University(QN2010002)

摘要/Abstract

摘要： A mathematical model of man-machine system is considered. Based on the reference [4], the direction and stability of the Hopf bifurcation are determined using the normal form method and the center manifold theory. Furthermore,the existence of Hopf-zero bifurcation is discussed. In the end, some numerical simulations are carried out to illustrate the results found.

关键词: man-machine system, stability, Hopf bifurcation, Hopf-zero bifurcation

Abstract: A mathematical model of man-machine system is considered. Based on the reference [4], the direction and stability of the Hopf bifurcation are determined using the normal form method and the center manifold theory. Furthermore, the existence of Hopf-zero bifurcation is discussed. In the end, some numerical simulations are carried out to illustrate the results found.

Key words: man-machine system, stability, Hopf bifurcation, Hopf-zero bifurcation

中图分类号:

O175.13

杨纪华, 刘媚. 具时滞人机系统的稳定性与分支分析[J]. 数学季刊, 2012, 27(2): 196-203.

YANG Ji-hua, LIU Mei. Stability and Bifurcation Analysis of Man-machine System with Time Delay[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(2): 196-203.

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