| 机床颤振模型时滞微分方程的稳定性与Hopf分支分析 |
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| 引用本文： | 杨纪华.机床颤振模型时滞微分方程的稳定性与Hopf分支分析[J].湛江师范学院学报,2013(6):10-15. |
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| 作者姓名： | 杨纪华 |
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| 作者单位： | 宁夏师范学院数学与计算机科学学院,宁夏固原756000 |
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| 基金项目： | 基金项目：国家自然科学基金资助项目（11031002）;宁夏自然科学基金项目（NZ13213）;宁夏师范学院创新团队资助项目（ZY201207）. |
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| 摘 要： | 从对系统线性化方程的特征方程根的分布分析入手，讨论了系统平衡点的稳定性，确定了系统的线性稳定性区域，发现当系统中的时滞经过一系列临界值时，系统经历了Hopf分支，并发现当时滞较大时，系统出现了混沌吸引子．最后，数值模拟验证了理论结果．
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| 关 键 词： | 时滞 稳定性 Hopf分支 混沌 |
Stability and Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations |
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| YANG Jihua.Stability and Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations[J].Journal of Zhanjiang Normal College,2013(6):10-15. |
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| Authors: | YANG Jihua |
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| Institution: | YANG Jihua (Department of Mathematics and Computer Science, Ningxia Normal University, Guyuan 756000, Ningxia, China) |
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| Abstract: | The stability of the equilibrium is discussed by analyzing the characteristic equation of the linear system of original system at the equilibrium, The regions of linear stability of equilibrium are given, it is found that Hopf bifurcation exist when the delay passes through a sequence of critical values and the chaos occurs when delay increase further. Finally, some numerical simulations are carried out for support- ing the analytic results. |
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| Keywords: | time delay stability Hopf bifurcation chaos |
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