| 具时滞正交切削颤振模型的稳定性与Hopf分支分析 |
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| 引用本文： | 杨纪华.具时滞正交切削颤振模型的稳定性与Hopf分支分析[J].井冈山大学学报（自然科学版）,2013(6):6-12. |
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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： | 宁夏自然科学基金项目（NZl32013）;宁夏师范学院创新团队项目（zy201207）;宁夏师范学院本科教学工程项目（JXGC2012801） |
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| 摘 要： | 研究了具时滞正交切削系统模型。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H0pf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构的正确性。
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| 关 键 词： | 时滞 稳定性 Hopf分支 混沌 |
STABILITY AND HOPF BIFURCATION ANALYSIS OF ORTHOGONAL CUTTING MODEL WITH TIME DELAY |
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| YANG Ji-hua.STABILITY AND HOPF BIFURCATION ANALYSIS OF ORTHOGONAL CUTTING MODEL WITH TIME DELAY[J].Journal of Jinggangshan University(Natural Sciences Edition),2013(6):6-12. |
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| Authors: | YANG Ji-hua |
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| Institution: | YANG Ji-hua (Department of Mathematics and Computer Science Ningxia Teachers University, Guyuan, Ningxia 756000, China) |
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| Abstract: | The mathematical model of orthogonal cutting model with time delay is studied. The stability of the equilibrium is discussed by analyzing the characteristic equation of the linearized 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 carded out for supporting the analytic results. |
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| Keywords: | time delay stability Hopfbifurcation chaos |
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