按照非线性理论，作者设计并实施了用于心脏系统非线性研究的深低温停循环（Profound Hy-pothermaia and Circulatory Arrest, 简称PHCA）实验。通过对PHCA实验中几个温度台阶上所采集的心电信号的功率谱分析和Lyapunov指数的计算，得出以下结论：（1）心电信息的功率谱和Lyapunov指数反映了心脏的总体动态特征，它们可用以估计心脏的健康状态；（2）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。

基于对一典型Langevin问题-在双势井和变化的磁场中并受-恒冲量不断作用的运动带电子粒子的动力学分的，利用频闪采样法，给出了描述粒子速度变化规律的复差分方程。选限适当的磁场强度和时间间隔（采样周期）。将这一差分方程简化为用来构造广义M_J（Mandelbrot_Julia）集的复映身，并基于粒子的动力学特征探讨了广义M_J集的物理意义。结果发现：1）广义M_J集的分形结构特征可形象地反映出粒子速度的变化规律；2）选限的时间间隔有、无意义、决定了广义M_J集的分形结构是否具有连续性；3）广义M_J集的演化，即粒子速度的变化规律依赖于相角主值范围的不同和选限；4）若改变磁场强度和时间间隔的选限，如选限一随机波动的磁场，则此时广义J集可能会出现内部被填充的结构特征，即在速度空间中粒子的不稳定周期轨道的闭包出现“爆炸”现象。

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。

According to the swiched complex mapping proposed by the author, the method constructing the switched processes generalized M (Mandelbrot) sets was elaborated, and a series of the switched processes generalized M sets for complex index number were constructed. The construction charaeteristies of the generalized M sets were expounded according to the analysis of teh algorithm constructing the generalized M sets. On the basis of what has already been achieved, the trajectories of a starting point in the complex C plane under the switched mapping were researched into, The results show the switched processes generalized M sets have the fractal feature, the construction characteristics of the switched processes generalized M sets are dependent on the complex number W and the switched variable ro, and the reaso which results in the discontinuity of switched processes generalized M sets is the discontinuity of choice of the pricipal range of phase angle.

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.