广义H non映射的滑模变结构控制同步

基于可线性化的非线性离散变结构跟踪控制方法实现了广义H non映射混沌系统的同步 .广义H non映射的混沌吸引子比H non映射的混沌吸引子要复杂得多 ,对于保密通信来说 ,这种复杂性正是所期望的 .提出的同步方法允许参数有适当的失配程度 ,这对工程实现是非常有利的 ,理论分析和仿真结果证实了该方法的有效性     

耦合映射混沌同步系统在加性噪声中的筛形域性态

由于实际系统中噪声不可避免，噪声使得同步混沌吸引子A变成具有一定生存时间<τ>的准稳态吸引子A′.以加性噪声作用下的二维耦合映射混沌同步系统为例，给定系统实验时间长 度T，解析发现：仅当<τ>>2T时准稳态同步混沌吸引子的筛形吸引域才可被定性观察到；而 当<τ><2T时则不复存在，此时，根据原无噪声时的筛形吸引域特征的不同，筛形域不仅可 以转变成时变筛形结构，还可以转变成分形结构.同时利用数值模拟作了进一步验证.该结果 对于二维耦合映射混沌同步系统具有普遍意义. 关键词： 混沌同步 筛形吸引域 瞬态混沌 耦合映射 加性噪声     

广义Hénon映射的滑模变结构控制同步

基于可线性化的非线性离散变结构跟踪控制方法实现了广义Hénon映射混沌系统的同步.广义Hénon映射的混沌吸引子比Hénon映射的混沌吸引子要复杂得多,对于保密通信来说,这种复杂性正是所期望的.提出的同步方法允许参数有适当的失配程度,这对工程实现是非常有利的,理论分析和仿真结果证实了该方法的有效性 关键词： 广义Hénon映射 混沌 同步 变结构控制     

广义Hénon混沌系统的自适应双模控制与同步

提出一种广义Hénon映射的自适应双模控制与同步方法.广义Hénon映射的混沌吸引子比Hénon映射的混沌吸引子更复杂,控制与同步困难,对于保密通信来说具有更高的安全性.该方法采用自适应双模控制,实现了广义Hénon映射的追踪控制与同步,提高了受控系统抑制参数摄动和随机扰动的能力,改善系统的鲁棒性.仿真结果验证了该方法的有效性.     

耦合帐篷映射混沌同步系统的筛形吸引域

讨论了两个线性耦合的标准帐篷映射混沌同步系统的同步混沌吸引子的吸引域,证明其是筛形吸引域.提出了筛形品质因子的概念,并据之给出了系统的同步混沌吸引子的吸引域发生 从局部筛形到全局筛形的转变的耦合参数临界值.修正了当系统出现筛形吸引域时的横截Lyapunov指数的解析表达式.指出考查筛形吸引域在混沌同步系统中有着重要意义. 关键词： 混沌同步 筛形吸引域 耦合帐篷映射     

SC混沌比例投影同步方法在保密通信中的应用

利用基于线性稳定性准则的SC混沌比例投影同步方法,提出一种应用于保密通信的混沌掩盖方案.适当分离出混沌系统的线性项与非线性项,构造一个非线性驱动向量函数,混沌状态变量包含用于投影同步的比例因子,把所需传递的有用信息掩盖入其中一个分量上,得到混沌载波信号,提高加密信息的复杂度和解码的困难度.以Lorenz吸引子和超混沌Rössler吸引子为例进行数值仿真,详细分析传输的正弦信息加密解密全过程,给出简单、最优的混沌掩盖方案,数值分析证明比例投影同步方法应用于保密通信领域的有效性.     

利用时空混沌同步进行数字加密通信

提出一种利用时空混沌同步的计算机网络数字加密通信方案,并用软件实现了语音双工实时密码通信.在该方案中,收、发端两个单向耦合映射格点(OCOML)系统被同一混沌信号所驱动而达到同步,其时空混沌输出信号分别用作加密和解密的密钥序列,OCOML的耦合参数为系统的主密钥.系统的主要优点是传输效率高,便于用软件实现实时通信,且通信的安全性获得了改善. 关键词： 时空混沌同步 密码系统 传输效率     

利用混沌信号幅值实现混沌同步

构造了一个三维混沌系统, 简要分析了该混沌系统的平衡点性质、混沌吸引子相图和Lyapunov指数等特性. 在此基础上, 利用反馈同步思想设计了一种利用混沌信号部分信息实现混沌同步的方法, 完成了三维混沌系统的同步. 该方法仅利用混沌信号幅值信息即可实现两个混沌系统的同步, 其同步建立与混沌信号的极性无关, 此特性可有效提高混沌通信质量. 通过分析系统的条件Lyapunov指数证实该方法的有效性, 数值仿真表明该方法与利用混沌信号全部信息的线性反馈同步法相比, 同步建立时间基本相同.     

声光双稳系统的混沌同步

首先给出布拉格型声光双稳系统耦合驱动的混沌同步化方案，用最大条件Ｌｙａｐｕｎｏｖ指数分析方法得出耦合驱动下系统混沌输出同步化条件，发现通过适当比例的耦合驱动可以使两组混沌系统达到同步的混沌输出。分析此混沌同步化方案可以抵抗噪声的干扰，并且在两系统出现偏差时仍可以实现混沌同步，找到了实用的单变量延时微分系统非Ｐｅｃｏｒａ－Ｃａｒｒｏｌｌ规则的混沌同步化方案。最后做了实验验证。     

基于单驱动变量的混沌广义投影同步及在保密通信中的应用

基于单向耦合提出一种只需传递一个驱动变量实现混沌系统广义投影同步方法.通过改变广义投影同步的比例因子,获得任意比例于原驱动混沌系统输出的混沌信号.由于只需传递一个信号,比起已有的方法具有更高的实用价值,理论推导和数值仿真进一步表明了该方法的有效性.最后,基于统一混沌系统的广义投影同步,给出了一种安全性更好的混沌保密通信方案. 关键词： 混沌系统 单驱动变量 广义投影同步 统一混沌系统     

Conversion of a chaotic attractor into a strange nonchaotic attractor in an one dimensional map and BVP oscillator

In this paper we investigate numerically the possibility of conversion of a chaotic attractor into a nonchaotic but strange attractor in both a discrete system (an one dimensional map) and in a continuous dynamical system — Bonhoeffer—van der Pol oscillator. In these systems we show suppression of chaotic property, namely, the sensitive dependence on initial states, by adding appropriate i) chaotic signal and ii) Gaussian white noise. The controlled orbit is found to be strange but nonchaotic with largest Lyapunov exponent negative and noninteger correlation dimension. Return map and power spectrum are also used to characterize the strange nonchaotic attractor.     

Scaling of intermittent behaviour of a strange nonchaotic attractor

We describe a type of intermittency present in a strange nonchaotic attractor of a quasiperiodically forced system. This has a similar scaling behaviour to the intermittency found in an attractor-merging crisis of chaotic attractors. By studying rational approximations to the irrational forcing we present a reasoning behind this scaling, which also provides insight into the mechanism which creates the strange nonchaotic attractor.     

Frequency locking by external force from a dynamical system with strange nonchaotic attractor

Usually, phase synchronization is studied in chaotic systems driven by either periodic force or chaotic force. In the present work, we consider frequency locking in chaotic Rössler oscillator by a special driving force from a dynamical system with a strange nonchaotic attractor. In this case, a transition from generalized marginal synchronization to frequency locking is observed. We investigate the bifurcation of the dynamical system and explain why generalized marginal synchronization can occur in this model.     

Recurrences of strange attractors

The transitions from or to strange nonchaotic attractors are investigated by recurrence plot-based methods. The techniques used here take into account the recurrence times and the fact that trajectories on strange nonchaotic attractors (SNAs) synchronize. The performance of these techniques is shown for the Heagy-Hammel transition to SNAs and for the fractalization transition to SNAs for which other usual nonlinear analysis tools are not successful.      

Experimental observation of strange nonchaotic attractors in a driven excitable system

We report the observation of strange nonchaotic attractors in an electrochemical cell. The system parameters were chosen such that the system observable (anodic current) exhibits fixed point behavior or period one oscillations. These autonomous dynamics were thereafter subjected to external quasiperiodic forcing. Systematically varying the characteristics (frequency and amplitude) of the superimposed external signal; quasiperiodic, chaotic and strange nonchaotic behaviors in the anodic current were generated. The inception of strange nonchaotic attractors was verified using standard diagnostic techniques.     

A lot of strange attractors: chaotic or not?

Iterations on R given by quasiperiodic displacement are closely linked with the quasiperiodic forcing of an oscillator. We begin by recalling how these problems are related. It enables us to predict the possibility of appearance of strange nonchaotic attractors (SNAs) for simple increasing maps of the real line with quasiperiodic displacement. Chaos is not possible in this case (Lyapounov exponents cannot be positive). Studying this model of iterations on R for larger variations, beyond critical values where it is no longer invertible, we can get chaotic motions. In this situation we can get a lot of strange attractors because we are able to smoothly adjust the value of the Lyapounov exponent. The SNAs obtained can be viewed as the result of pasting pieces of trajectories, some of which having positive local Lyapounov exponents and others having negative ones. This leads us to think that the distinction between these SNAs and chaotic attractors is rather weak.     

A special type of attractor and transitions in a delayed system

We discuss strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors in a quasiperiodically driven system with time delays. A route and the associated mechanism are described for a special type of attractor called strange-nonchaotic-attractor-like (SNA-like) through T² torus bifurcation. The type of attractor can be observed in large parameter domains and it is easily mistaken for a true SNA judging merely from the phase portrait, power spectrum and the largest Lyapunov exponent. SNA-like attractor is not strange and has no phase sensitivity. Conditions for Neimark-Sacker bifurcation are obtained by theoretical analysis for the unforced system. Complicated and interesting dynamical transitions are investigated among the different tongues.     

非周期力在混沌控制中的双重功效

探讨了非周期力（有界噪声或混沌驱动力）在非线性动力系统混沌控制中的影响.以一类典型的含有五次非线性项的Duffing-van der Pol系统为范例,通过对系统的轨道、最大Lyapunov指数、功率谱幅值及Poincar截面的分析,发现适当幅值的有界噪声或混沌信号,一方面可以消除系统对初始条件的敏感依赖性,抑制系统的混沌行为,将系统的混沌吸引子转化为奇怪非混沌吸引子;另一方面也可以诱导系统的混沌行为,将系统的周期吸引子转化为混沌吸引子.从而揭示了非周期力在混沌控制中的双重功效：抑制混沌和诱导混沌. 关键词： 混沌控制 有界噪声 混沌驱动力     

Nonchaotic random behaviour in the second order autonomous system

Evidence is presented for the nonchaotic random behaviour in a second-order autonomous deterministic system. This behaviour is different from chaos and strange nonchaotic attractor. The nonchaotic random behaviour is very sensitive to the initial conditions. Slight difference of the initial conditions will generate wholly different phase trajectories. This random behaviour has a transient random nature and is very similar to the coin-throwing case in the classical theory of probability. The existence of the nonchaotic random behaviour not only can be derived from the theoretical analysis, but also is proved by the results of the simulated experiments in this paper.     

Anticontrol of chaos in continuous-time systems via time-delay feedback

In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure. (c) 2000 American Institute of Physics.