判定非自治Birkhoff系统稳定性的广义组合梯度方法

研究判定非自治Birkhoff系统稳定性的广义组合梯度方法．首先，给出非自治Birkhoff系统和非自治广义Birkhoff系统的运动微分方程；其次，给出一类将广义梯度系统和广义斜梯度系统组合而成的广义组合梯度系统，并讨论广义组合梯度系统的一些性质；最后，将非自治Birkhoff系统和非自治广义Birkhoff系统在一定条件下表示成广义组合梯度系统，并用广义组合梯度系统的性质研究了这两类Birkhoff系统的稳定性．举例说明结果的应用．

A Generalized Combinatorial Gradient Method for Determining the Stability of Non-Autonomous Birkhoffian Systems

A generalized combinatorial gradient method for determining the stability of non-autonomous Birkhoffian systems is studied. Firstly, The differential equations of motion for a non-autonomous Birkhoffian system and a non-autonomous generalized Birkhoffian system are given; Then, a generalized combined gradient system has been proposed, and the property of the system has been studied; Finally, the non-autonomous Birkhoffian system and the non-autonomous generalized Birkhoffian system are expressed as generalized composite gradient systems under certain conditions, and the stability of these two kinds of Birkhoff systems is studied by the properties of the generalized combined gradient system. Two examples are given to illustrate the application of the results.