| 判定广义Birkhoff系统稳定性的三重组合梯度方法 |
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| 引用本文： | 董孟峰,陈向炜.判定广义Birkhoff系统稳定性的三重组合梯度方法[J].上海力学,2019,40(3):543-548. |
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| 作者姓名： | 董孟峰 陈向炜 |
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| 作者单位： | 苏州科技大学数理学院,江苏苏州,215009;商丘师范学院电子电气工程学院,河南商丘,476000 |
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| 基金项目： | |
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| 摘 要： | 研究判定广义Birkhoff系统稳定性的三重组合梯度方法．首先，给出4类三重组合梯度系统的定义和微分方程；其次，得到广义Birkhoff系统成为三重组合梯度系统的条件，从而将广义Birkhoff系统化成三重组合梯度系统；最后，利用组合梯度系统的性质来研究系统的稳定性，举例说明结果的应用．
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| 关 键 词： | 广义Birkhoff系统 三重组合梯度系统 稳定性 |
Triple Combined Gradient Method for Determining the Stability of Generalized Birkhoff Systems |
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| DONG Mengfeng,CHEN Xiangwei.Triple Combined Gradient Method for Determining the Stability of Generalized Birkhoff Systems[J].Chinese Quarterly Mechanics,2019,40(3):543-548. |
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| Authors: | DONG Mengfeng CHEN Xiangwei |
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| Abstract: | A triple combined gradient method is studied to determine the stability of generalized Birkhoff systems. Firstly, the definitions and differential equations of four classes of triple combined gradient systems are given. Secondly, the conditions for generalized Birkhoff system to be a triple combined gradient system are obtained. Thus, the generalized Birkhoff system is transformed into a triple combined gradient system. Finally, the stability of the system is studied by using the properties of the triple combined gradient system. The application of the results is illustrated by four examples. |
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| Keywords: | generalized Birkhoff system triple combined gradient system stability |
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