动力学系统中非线性项的跳跃随机性

计算机计算和实验的结果表明:动力学系统中非线性函数有一种特殊性质,即跳跃随机性。这种性质使确定的非线性函数中产生了许多不同于自身曲线的跳跃随机曲线。

跳跃随机性在倍周期分岔运动中的表现

动力学系统中分岔与混沌现象产生的必要条件之一，就是该系统必须是非线性的。而该系统中的非线性元件和非线性函数项有一个特殊性质，即跳跃随机性。跳跃随机性是确定的非线性函数项和确定的非线性元件所特有的内随机源。作者通过二阶单结管电路的实验及对其数学模型进行的计算机计算，观察了在倍周期分岔和混沌运动中，非线性函数项和非线性元件所表现的跳跃随机性及跳跃随机曲线的某些特点和规律。

A Novel Complexity Metric of Frequency Hopping Sequences

This paper made use of approximate entropy (ApEn) to evaluate the complexities of frequency-hopping (FH) sequences. By defining the maximal randomness of sequences with arbitrary lengths, ApEn can classify different complex systems including stochastic processes, deterministic random process and random processes. It modified the conventional ApEn, which is used for continuous data sequence, for the discrete FH sequences. Two important theorems were given and the related main parameters were discussed. The algorithm was tested with several families of FH sequences. The simulation results show that ApEn is able to discern the changing complexities of FH sequences with a relatively small amount of samples of sequences.

单结管电路在周期激励下的临界动态研究

非线性系统在临界点附近存在有意义的动态行为，实验采用单结管作为非线性元件和周期信号作为扰动源；观察非线性元件的动态轨迹在临界点附近的动态。一旦变化控制参数使非线性元件的动态轨迹越过临界点后，电路能产生丰富的非线性模态。非线性元件的动态轨迹越过临界点后便产生随机跳跃曲线，这些随机跳跃曲线的形状可分为三类Ｃａｎａｒｄ极限环轨迹。在临界点附近，非线性元件的动态轨迹的负阻段有一个临界阈值区域，经过此区域的轨迹跳跃分离成不同类型和不同尺度的Ｃａｎａｒｄ曲线。