时变周期大系统的平稳振荡

On the Harmonic Oscillations of Large-scale Time-varying Periodic Systems

本文讨论时变周期大系统的周期解,得到两个充分性判据,我们的方法是“平均法”、工具是J|fJryHoB函数。结果表明,若各孤立子系统的平均系统有平稳振荡,系数矩阵振幅较小各系统之间的关联较弱,则大系统亦存在唯一的平稳振荡。

In this pqper, we discuss the periodic solutions of large-scale time-varying periodic systems, we obtain two criteria for the existence of periodic solutions. Our method is the'Method of averaging', our tools are Liapunov's functions, we prove that, if there exists harmonic oscillation for each subsystem in a large-scale system and the correlation terms arc small, there must exists unique harmonic oscillation for the large-scale system.