双参数对广义Hamilton系统稳定性的影响

Influence of Double Parameters on the Equilibrium Stability of Generalized Hamilton Systems

研究双参数对带附加项的广义Hamilton系统稳定性的影响.首先将该系统在一定条件下化成梯度系统.其次利用梯度系统的特性来研究这类系统的稳定性及其对双参数的依赖关系.再次在参数平面给出稳定性区域.结果表明,该系统的平衡稳定性随双参数变化可能是稳定的,或渐近稳定的,也可能是不稳定的,相应给出各种稳定性对应的参数变化范围.

Influence of double parameters on the equilibrium stability of generalized Hamilton systems with additional terms was studied. Firstly, a generalized Hamilton system with additional terms was considered as a gradient system under certain conditions. Secondly, the char- acteristics of the gradient system was used to study the equilibrium stability and its dependance on the two parameters of the system. Thirdly, the stability domain was given in the parameter plane. The results show that the equilibrium of the system is likely to be stable, or asymptotical- ly stable, or even unstable with the change of the two parameters, and the range of parameters corresponding to each equilibrium state is given.