照非线性理论，对健康人冠心病人和成年犬进行了心电取样，在对人和犬的大量心电信号的功率谱分析关联维数和Lyapunov指数计算的基础上，通过对比研究，得出以下结论：（ⅰ） 心电信号的功率谱关联维数和Lyapunov指数反映了心脏的总体动态特征，它们可作为一种定量研究心电图的新方法进行心血管疾病的早期诊断。（ⅱ）在正常的生理状态下心脏的运动是混沌的，而在病理状态下则趋于有序。（ⅲ）基于人犬对比，揭示出混沌是衡量生物体制进化的一个定量指标。

In orderlo stody the iatefior strcture of the Mandelbrot (M) set. Pickover and Hooper have ad-wwed the epsilon cross method and the star trails method. respectively. In order to reveal the exterior structure of the Mset. Philip has proposed the regional decomposition method and the angle-slicing decompoaition method. In this pa-per. these methods-are extended. and the equipolenfial line method and the color adjustment method are proposod to study the exterior struture of the M set. A series of the non-boundary region structure images of the generalized M sets is generated by using the above-mentioned methode. The results show that the non-boundary regions of the generalized M sets for intexer index number have the fraetal feature; while those for decimal index number have diseontlnuity and col-lapse, and their erolutions depend on the choice of the principal range of the phase angle.

In order to show details of fractal structure of Mandelbrot set precisely, Lyapunov exponents and periodic scanning techniques have been brought forward by Shirri and Welstead. This paper generalizes these two techniques and puts forward periodicity orbit search and comparison technique which can be used to discuss the relationship of the generalized Mandelbrot–Julia sets (the generalized M-J sets). Adopting the techniques mentioned above and the experimental mathematics method of combining the theory of analytic function of one complex variable with computer aided drawing, this paper researches on the structure topological inflexibility and the discontinuity evolution law of the generalized M-J sets generated from the complex mapping z→zα+c(α∈R), and explores structure and distributing of periodicity "petal" and topological law of periodicity orbits of the generalized Msets, and finds that the generalized Mset contains abundant information of structure of the generalized J sets by founding the whole portray of the generalized J sets based on the generalized Mset qualitatively. Furthermore, the physical meaning of the generalized M-J sets have been expounded.

为探讨Mandelbrot集（简称M集）的内部结构，推广了Pickover和Hooper的“ε正交”法和“星迹”法；及Philip的“区域分解”法和“角度分解”法并提出了用于研究M集外部结构的等势线法和色彩调配法利用上述方法，构造了一系列广义M集非边界区域的结构图研究表明整数阶广义M集的非边界区域具有分形特征，小数阶广义M集的非边界区域出现了错动和断裂，且其演化过程依赖于相角主值范围的选取。

阐述了构造复映射z←zα+c（α<o）所产生的广义Mandelbrot-集（简称M-集或M-分形图）的逃逸时间算法。通过改变参数α，作出了一系列有趣的分形图这些分形图为若干卫星群环绕中央恒星的星群结构。定量地研究了恒星和卫星群的几何结构，并对α取非整数时分形图的结构特点和卫星群胚胎出现的原因进行了分析。最后给出几点结论。