混沌

And then, in the foundation of the overseas scholars'study, I study RP and the CRP methods for visualization the dynamics characteristic of the phase space track as well as the complexity degree algorithm of chaos time series——ApEn algorithm. Applying these two methods based on the VB program we analyze separately the data which is obtained from complex financial system model and Lorenz system, and obtain several new recurrence plots and cross recurrence plots. This provides the graph gist of determination complex intrinsic characteristic. The results establish the foundation for exact and further division of chaos time series.

接下来，在国外学者研究的基础上，基于混沌时序形象化相空间轨迹的动力学特征的分别研究了RP和CRP方法以及判定混沌时间序列的复杂度算法的ApEn算法，基于VB程序应用这两种方法分别对Lorenz系统及实际的一类复杂金融系统模型所得到的数据进行了分析，得到了几个较为新的复原图和相干复原图，这对于判定时序数据的复杂内在特性提供了图形上的比对依据，研究结果为混沌时序的准确和进一步分类奠定了基础。

Those figures indicate that when delay is very small, the stability of steady states doesn't change and chaos still exist. As delay increases, the stability of steady states is changed. When delay is near some critical value, a family of periodic solutions bifurcate from the steady state.

这些系统的相图显示了当时滞为零或者时滞很小时，平衡点的稳定性没有发生变化，于是轨道的混沌震荡也没有发生改变，而当时滞逐渐增大时，系统的混沌特性会发生变化，在τ取某些值时，混沌震荡会演变为一个稳定周期轨道。

In the last chapter, on the basis of theories in paper [4, 5], the notions of strong mixing, weak mixing, generator and expansion of the variable-parametric dynamical system are introduced, it turns out that in variable-parametric dynamical system strong mixing implies weak mixing and then implies transitivity; it is proved that if and both are variable-parametric dynamical system, F conjugates with G , the members of F are communicate with each other and the members of G are also communicate with each other, what's more, they are both homeomorphism, then F is strong mixing implies G has the same properties; futhermore, we prove that F is strong mixing implies F Devaney chaos in the sense of modification in variable-parametric dynamical system and that F Devaney chaos in the sense of modification if and only if G Devaney chaos in the sense of modification when semi-conjugate with and they both are communicate and homeomorphism; at last, we illustrate that F has generator if and only if it has weak generator, and we also prove that if F is expansion, then F has generator.

在第三章中，我们在文[4，5]的基础上，提出了变参数动力系统拓扑强混合、拓扑弱混合以及变参数动力系统的生成子、扩张的概念；证明了变参数动力系统拓扑强混合蕴含拓扑弱混合，进而蕴含拓扑传递；证明了：如果，为两个变参数动力系统，F与G拓扑半共轭，且F两两可交换，G两两可交换，它们均为同胚映射，那么F拓扑强混合，则G也有同样的性质；本章还证明了变参数动力系统拓扑强混合蕴含F在修改的意义下Devaney混沌；在此基础上得出了：如果变参数动力系统与变参数动力系统拓扑半共轭，它们都两两可交换，并且它们均为同胚映射，那么F在修改的意义下Devaney混沌当且仅当G在修改的意义下Devaney混沌；得出了F有生成子当且仅当F有弱生成子；如果F是扩张的，则F有生成子。

Because the chaos is characterized by"supersensitivity"to the initial conditions and long term forcasts of trajectories are impossible, control of chaos becomes the essential link to application.

由于混沌运动具有初值敏感性和长时间发展趋势的不可预见性，混沌控制就成为混沌应用的关键环节。

In the meantime, we got several achievements during the process:Firstly, a sequence encryption algorithm of real-time video in use of one dimension piece-wise linear chaotic map is carried out. This algorithm makes use of Inter' s SSE2 special dictates and makes nonlinear change of chaotic sequences.As a result, the algorithm not only encrypts faster, but also resists several cipher analysis methods. Secondly, this paper presents a block encryption algorithm of real-time video based on chaotic neural network which makes use of numerical transient chaotic neural network to produce chaotic sequences and uses these sequences to do encryption.

同时，在实现系统的过程中，取得了以下研究成果：(1)提出了一种利用一维的分段线性混沌映射来对实时视频进行序列加密的算法，该算法利用Inter的SSE2专用指令集来实现，并对产生的混沌序列进行了有效的非线性变换，从而使该算法不仅加密速度快，并且能有效的抗多种密码分析；(2)提出了一种利用混沌神经网络对实时视频进行分组加密的算法。

We can control the lower bound of the extended cycle length by choosing the appropriate m-sequences as perturbation sequences.

同时，我们可以通过控制混沌系统输出的m序列的长度来控制混沌序列的最小周期，以产生满足我们需要的混沌序列。

Then, the dynamic behaviors of Lur'e system have been analyzed through the simulation method, and the paper presents that the final dynamic behaviors of the system are sequentially changed according to the following states: the unstable dispersing state, chaotic state, steady cycle state and balanced state respectively with the filtering wave function from weak to strong and under the condition of meeting parameters.

以一维逻辑斯蒂方程为工具，论证了一类非线性Lur'e系统通过周期倍化达到混沌的机制，深入研究了该系统由混沌转化为有规律的周期性问题，并通过仿真分析了Lur'e系统的动力学行为，得出了这类系统在满足参数条件下，随着滤波作用的由弱到强，系统的最终动力学行为依次按着不稳定的发散状态、混沌状态、稳定的周期态、平衡态的顺序变化。

By extending the method of the perturbation control applied to 1-D systems to 2-D discrete dynamical systems, we study its control on spatial chaos in the sense of space.

空间混沌的参数微扰控制将一维系统的参数微扰控制拓展到2-D离散动力系统上，真正从空间意义上研究2-D离散动力系统的混沌控制，实现了其空间混沌的控制，并利用Lyapunov第一方法给出了不动平面稳定的一个充分条件。

Assumptions: theright to a permanent Christmas Antlers hit a Christmas special Antlers scroll attributes of a multi-force attacks a magicpower until after a chaotic time scroll (scroll Chaos: 60% of the property was an increase of 5 or 5) If another 2 smashingsuccess of the chaotic volume increases are aggressive, and that Christmas is the ability to attack the Moluccan 1 +5 +5 = 11attack.

假设：一个永久权的圣诞鹿角砸中了一张圣诞鹿角专用卷轴属性多了 1攻击力 1魔法力等到以后出混沌卷轴的时候（混沌卷轴：60%随即属性增加5或减少5）如果能再砸成功2张混沌卷都加攻击力，那圣诞鹿加的攻击力就是 1+5+5=11攻。11攻的帽子价格会怎么样大家自己想吧'''''''''但是注意，以上的只是假设而已。

Also known as Spawn of Chaos , the Chaos Spawn is a nasty-looking monstrosity from the Realm of Chaos , living only through the forces of pure chaos that keep its mutated and mutilated body together.

混沌菌种是一种因为受到太多的混沌诸神祝福而最终失去心智的怪物，它们即使不在战斗中战死，也会在最后被扭曲的混沌诸神的力量而撕裂。

Objective: To study the effect of polycythemia on blood oxygen saturation.

裴蕾目的：观察RBC剧增而引起的高粘血症对血氧饱和度的影响。

Based on SIMPLER algorithm in the curvilinear body-fitted coordinates, the calculations were performed for Pr=0.7, Re=10~1000 on non-orthogonal non-staggered grids which are generated by elliptic equation systems.

采用曲线坐标系下压力与速度耦合的SIMPLER算法，数值研究了周期性渐扩渐缩波纹通道内脉动流动与换热情况，流动Re数的范围为10~1000，Pr数为0.7。