空间单位区域双二次有理贝赛尔曲面混沌特性研究

Chaos analysis of the rational Bzier biquadratic surface in the unit area

研究空间单位区域内两个二次曲面映射构成的函数的混沌特性,发现了一种构造混沌的方法.当一个曲面是单位区域内标准曲面,另一个曲面随机生成时,此函数是混沌的概率可以大于十分之一,说明在满足一定条件时,混沌是极其普遍的.通过计算Lyapunov指数以及绘制分岔图等对该类函数的混沌特性进行分析,根据参数变化的分岔图以及混沌曲面控制点的区域分布特性等寻找混沌映射函数,得到了大量的二维混沌吸引子图形,并对其中三个进行了详细研究.另外,把灰度图像作为离散二维函数,首次研究了图像作为迭代表达式时表现出的一些混沌特性.研究发现,相同的或者相近的图像易于收敛到周期点上,这个结果可以用于图像识别等研究领域.

In the paper, the chaotic characteristics of two functions are studied by a quadratic surface mapping in spatial unit area. When a surface is the standard surface in spatial unit area and another surface is generated randomly, the probability that the two functions are in the chaos can be greater than one-tenth, so this is a better method of generating chaos. The chaotic characteristics are analyzed by calculating the Lyapunov exponent and drawing the bifurcation diagram. According to the bifurcation diagram of the changing parameter and the characteristics of the regional distribution of the chaotic surface control points, the chaotic mapping function can be found and a lot of two-dimensional chaotic attractor graphics can be obtained. Besides, gray scale image is regarded as a discrete two-dimensional function for the first time. The study of image as an iteration expression shows some chaotic characteristics. The study shows that the same or similar image converges to the cycle point easily, which can be used in some research areas such as image recognition.