离散大系统在结构扰动下周期解的存在性

对于离散系统稳定性的研究,近年来受到人们的重视,但对于周期解的研究,在文献中还很少看到。本文首先讨论了离散系统解的有界性,并且得到了若一个具有周期系数的差分方程的解为最终有界的,则存在周期解的结果。然后利用李雅普诺夫函数方法研究了离散大系统在结构扰动之下周期解的存在性和离散大系统的平稳振荡。

The Existence of Periodic Solutions of Large-scale Discrete Systems under Structural Perturbations

The stability of Large-scale discrete systems has been deeply studied for recent years, the study of their periodic solutions, however , remains untouched. The dissertation firstly considers the boundness of solutions of large scale discrete systems. It is proved in this paper there exists a periodic solution if the solutions of the difference equation with periodic coefficients are ulfimate boun ded. Using the method of Liapunov functions, the dissertation then studies the existence of periodic solutions of large-scale discrete systeme.