Existence of heteroclinic orbits in a novel three-order dynamical system

In this paper,we design a novel three-order autonomous system.Numerical simulations reveal the complex chaotic behaviors of the system.By applying the undetermined coefficient method,we find a heteroclinic orbit in the system.As a result,the Si’lnikov criterion along with some other given conditions guarantees that the system has both Smale horseshoes and chaos of horseshoe type.     

Construction of Generalized Synchronization for a Kind of Array Differential Equations and Applications

Chaos synchronization, as a special complex phenomenon, has been studied for about a decade. Only recently, have generalized chaotic synchronization phenomena been realized to be general in the real world and to have potential applications. We present two theorems for constructing a kind of array differential equations with generalized synchronization (GS) with respect to linear transformations. Two array differential equation systems with GS are introduced based on our theorems. Numerical simulations show that the two systems display periodic GS and chaotic GS, respectively.     

A Topological Degree for Multivalued Generalized A-proper Mappings

The aim of this note gives a generalization of the degree theory for single valued G-A-proper mappings of [4] and a degree theory for multivalued G-A-proper mappings. Let (X,Y) be a pair of separable Banach spaces with given approximation scheme {X_n, Y_n, Q_n} ([2] Section2). Let D be an open bounded subset of X.     

Generalized Synchronization of Time-Delayed Differential Systems

We establish two theorems for two time-delayed （chaotic） differential equation systems to achieve time-delayed generalized synchronization （TDGS）. The theorems uncover general forms of two TDGS systems via a prescribed differentiable transformation. Based on the theorems, we use two-coupled Ikeda equations as the driving system to construct TDGS driven systems via two prescribed transformations. Numerical simulations demonstrate the effectiveness of the proposed theorems. It may be expected that our theorems provide new tools for understanding and studying TDGS phenomena.     

S-盒的Lyapunov指数研究

在密码算法的设计中,S-盒有着信息混淆的重要功能.传统的S-盒的密码学指标一般包括线性偏差、差分特征、代数免疫度、不动点个数、雪崩效应等.2006年,Kocarev给出了有限集合上的离散混沌理论.本文借鉴该理论,在汉明距离的基础上给出了S-盒的Lyapunov指数的定义,利用该定义计算了几个密码算法中的S-盒的Lyapunov指数值,并进行了比较.证明了在欧氏距离上定义的Lvapunov指数最大的映射,按本文提出的S-盒的Lyapunov指数的定义其Lyapunov指数为0;讨论了S-盒的Lyapunov指数与S-盒的雪崩效应之间的关系,该关系实际上是混沌理论中的蝴蝶效应与密码学中的雪崩效应之间的关系.本文提出的S-盒的Lyapunov指数的定义可视为对传统的S-盒的密码学指标的补充.     

Fibonacci序列在准晶体结构研究中的应用

1984年底关于具有五次对称的准晶态的发现,冲破了一百多年来建立起来的经典晶体学的现有理论基础.在随后得到的锰-铝准晶体高分辨电子显微图中,呈环状分布的亮点在直线方向或相间或重叠,而结点分布服从 Fibonacci 排列.本文介绍了含有五次对称的新点群和新单形;研究了 Fibonacci 排列的一些性质;提出了一个有趣的排队规则,证明了有关的定理,从而较圆满地描述了准晶体结构的一些特征.     

A Chaotic Communication Scheme Based on Generalized Synchronization and Hash Functions

A new chaotic communication scheme based on generalized chaotic synchronization (GCS) and hash function transpositions is presented. The communication scheme has nonsymmetric secrete keys and its ability is similar to traditional digital signatures, i.e. a receiver can convince himself whether or not the sender‘s message contents have been modified. As a direct application of the scheme, a GCS system is designed by using Chen‘s chaotic circuit and is studied in some detail. The numerical simulation shows that this Chen GCS system has high security and is fast and reliable for secure lnternet communications.     

准晶体的晶胞构成及准晶格的推导

本文从结晶化学原理及二十面体相出发,提出了八次对称准晶体中可能存在的两种配位多面体形式——三角十六面体及带帽反棱柱。推导了该类准晶体的一维及二维准晶格。运用传统结晶学中定义Bravais晶胞的原则定义了准晶体中五次、十次、八次、十二次对称准晶体的四种二维准晶胞。本文作者认为准晶体实际上是具无公度平移周期的晶体,该类晶体的无公度平移对称,是通过放大或缩小这两种具分数维特征的对称操作来实现的。     

多面体的几何参数与八次、十二次对称准晶

本文研究12n面体、4n面体和2n+2面体的几何参数.这些多面体诸顶点在x-y平面的设影均呈2n 次对称.当 n=4,6时得出8种多面体.期望它们可有助于用来研究新建发现的具有8次、12次对称的新准晶.