The bifurcation threshold value of the chaos detection system for a weak signal＊

Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detectionsystem for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detectionare correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system fora weak signal is established by using the theory of linear differential equation with periodic coefficients and computingthe Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system isdefined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of thechaos detection svstem.     

一类耦合非线性振子同步混沌Hopf分岔及其电路仿真

对于一类同时存在扩散耦合和梯度耦合的非线性振子系统, 通过空间傅里叶变换，得到具有不同波矢的各运动模式的相互独立的运动方程. 计算各横截模的Lyapunov指数, 可在耦合参数平面上确定同步混沌的稳定区域. 在稳定区域边界, 一对共轭横截模式失稳，导致同步混沌的Hopf分岔. 对耦合Lorenz振子系统进行了数值模拟，并设计了耦合Lorenz振子系统的电路, 进行耦合振子系统同步混沌Hopf分岔的电路仿真实验. 计算和仿真的结果表明，Hopf分岔的特征频率等于失稳横截模式的振荡频率. 关键词： 耦合非线性振子 同步混沌 横截模式 电路仿真     

竖直振动颗粒物厚层中冲击力分岔现象

实验研究了竖直振动颗粒物厚层中颗粒对容器底部的压力. 发现这种压力是脉冲式的，并表现出受振动加速度控制的倍周期分岔现象. 在颗粒层底部观察到颗粒密堆积在一起的聚集态. 聚集态内颗粒的自由程较小，并像一个整体一样运动. 关键词： 颗粒物质 混沌 倍周期分岔 非弹性碰撞     

光纤混沌相位编码保密通信系统理论研究

通过耦合激光混沌相位控制同步系统和光纤信道，提出外部光注入半导体激光器激光混沌相 位控制光纤同步以及混沌相位相移键控外调制光纤保密通信系统理论模型，数值实现了在相 位控制器控制下的远程光纤混沌同步.理论分析了光纤自相位调制对混沌信号以及对同步的 影响，导出了光纤混沌最大传输距离公式.通过连续键控调制相位控制器实现了光纤激光混 沌相位相移键控编码调制发射，设置接收系统相位控制器控制激光相位相移实现了光纤激光 混沌同步解调.数值模拟了具有比特率50Mbit/s远程光纤混沌数字编码通信系统的应用，详 细地进行了在远距离光纤传输中的系统参数失配以及系统抗噪声能力的数值分析. 关键词： 混沌 同步 光纤混沌通信 半导体激光器 相位     

周期轨迹与不可积体系的量子化：Henon-Heiles体系的一个研究例子

研究了两个振子耦合的Henon-Heiles体系的周期轨迹与量子化问题.结果表明，周期轨迹的 作用量积分与体系的能量有着简单的线性关系.可以利用那些是整数值的周期轨迹的作用量 积分对不可积体系进行半经典量子化.由周期轨迹的物理内涵出发，揭示混沌体系的残余周 期轨迹具有与量子化有关的性质.这对于认识和理解经典力学与量子体系的联系关系及其物 理内涵有着深刻而重要的意义. 关键词： 周期轨迹 半经典量子化 混沌     

一种提取光反馈混沌激光器时延信息的谱分析方法

鉴于时延信息严重威胁着混沌通信的保密性,提出了一种利用频谱仪直接确定激光器时延信息的新方法。通过记录和观察信号的频谱,发现其频谱受到了时延信息的调制;进一步对频谱作逆傅里叶变换,即可直接获取光反馈混沌激光器的时延信息。实验中对腔长L=11.02 m的单反馈和腔长近似相等(L1=11.02 m, L2=11.25 m)或腔长成整数比(L1=11.02 m, L2=22.03 m) 的双反馈情形进行了研究。分析结果表明:在两外腔长度近似相等的情况下,2个外腔长度信息不能被隐藏;当反馈外腔长度成整数比时可以从频谱中提取出半导体激光器的反馈延迟时间。     

Addendum to “Spatiotemporal evolution in a (2+1) -dimensional chemotaxis model” [Physica A 391 (2012) 107–112]

After our article, Physica A 391 (2012) 107–112, had been published online, T. Hillen told us about a theorem by Osaki, relevant for our numerical simulations.     

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.     

Evidence of Strange Attractors in Class C Amplifier with Single Bipolar Transistor: Polynomial and Piecewise-Linear Case

This paper presents and briefly discusses recent observations of dynamics associated with isolated generalized bipolar transistor cells. A mathematical model of this simple system is considered on the highest level of abstraction such that it comprises many different network topologies. The key property of the analyzed structure is its bias point since the transistor is modeled via two-port admittance parameters. A necessary but not sufficient condition for the evolution of autonomous complex behavior is the nonlinear bilateral nature of the transistor with arbitrary reason that causes this effect. It is proved both by numerical analysis and experimental measurement that chaotic motion is miscellaneous, robust, and it is neither numerical artifact nor long transient motion.     

Positive and negative Hanbury-Brown and Twiss correlations in normal metal-superconducting devices

In the light of the recent analogs of the Hanbury-Brown and Twiss experiments [1] in mesoscopic beam splitters, negative current noise correlations are recalled to be the consequence of an exclusion principle. Here, positive (bosonic) correlations are shown to exist in a fermionic system, composed of a superconductor connected to two normal reservoirs. In the Andreev regime, the correlations can either be positive or negative depending on the reflection coefficient of the beam splitter. For biases beyond the gap, the transmission of quasiparticles favors fermionic correlations. The presence of disorder enhances positive noise correlations. Potential experimental applications are discussed. Received 1 June 1999