IFS吸引子的界与其动力学性态的研究

Boundary of Attractors of Iterated Function Systems and Its Dynamic Characteristics

阐述了迭代函数系(IteratedFunctionSystem,简称IFS)理论及随机迭代算法,通过理论解析给出了求IFS吸引子界的方法,介绍了IFS吸引子的Lyapunov指数和关联维数的算法。利用计算机构造了一系列IFS吸引子,计算了IFS吸引子的界、Lyapunov指数和关联维数,分析了IFS吸引子的动力学特征,讨论了当参数变化时IFS吸引子界的变化规律。

The iterated function systems （it is called ITS for short） theory and the random iteration algorithm were expounded. By the theory analysis, the method by which the boundary of attractors of ITS can be evaluated was given out. The algorithm of determining the lyapunov exponent and the correlation dimension of the attractors of ITS was introduced. Utilizing the computer simulated a series of the attractors of ITS. The boundary, the lyapunov exponent and the correlation dimension of the attractors of ITS were calculated, and the dynamic characteristics of the attractors of ITS were analyzed. The changing regularity of the boundary of attractors of ITS was discussed when the control parameters were changed.