一种参数摄动的混沌异结构同步方法

研究了参数摄动情形下的混沌异结构同步问题,基于Lyapunov稳定性定理并结合范数理论给出了系统参数摄动下实现混沌异结构同步的一个充分条件,为同步控制器的设计提供了一般方法.只要两混沌系统维数相等,状态变量可测,就可利用所提方法实现系统参数摄动下的异结构同步,并能够保证在同步实现后同步控制量伴随误差变量一同收敛至零.该方法鲁棒性强,适用范围广,通过对混沌系统、超混沌系统的同步仿真,证实了该方法的有效性. 关键词： 混沌 超混沌 同步 Lyapunov函数     

混沌系统的速度反馈同步

从线性反馈同步、广义同步、耦合同步三个方面讨论了混沌系统的速度反馈同步，计算了速度反馈同步所需要满足的反馈系数的条件，并与一般意义下的位移反馈同步系数进行了比较，结果表明速度反馈系数均大幅度减小，从而降低了同步的复杂度和代价.数值仿真表明了该方法有效可行. 关键词： 混沌 反馈 同步 最大Lyapunov指数     

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.     

时空混沌的单向耦合同步

以耦合映象格子模型为例,提出利用单向耦合驱动时空混沌的同步方案,并进行了数值分析.结果表明,适当地选择耦合驱动强度因子和均衡系数,两个时空混沌系统可以达到准确同步.通过计算最大条件Lyapunov指数,给出了可实现时空混沌同步的最小耦合强度以及最小耦合强度与系统参数之间的关系曲线.数值模拟还证明,此方法工作鲁棒 关键词： 时空混沌 同步 单向耦合 最大条件Lyapunov指数 数值模拟     

一种超混沌映射的单双参量自适应同步

利用参量自适应法实现了超混沌系统Kawakami映射的同步.通过严密的数学推导,给出了Kawakami映射在单参量自适应下实现同步的充分条件,并在双参量自适应控制下系统同样实现了同步.数值模拟结果显示,该映射输出具有类似于白噪声的宽谱特性,因此比较适合用于保密通信.     

统一混沌系统的反馈同步

应用线性、非线性和广义同步三种反馈方法,研究了一个新的单参数统一混沌系统的反馈同步问题.研究表明,线性反馈同步和广义同步中控制参数k的下确界与系统的最大Lyapunov指数λ有关,并且导出了非线性反馈同步的控制参数p,q与统一系统参数α的关系.数值仿真表明反馈同步方法的有效性和理论结果的正确性. 关键词： 统一混沌系统 反馈同步 控制 最大Lyapunov指数     

超混沌振荡器的混沌耦合同步

提出了两种应用单变量单向混沌耦合同步超混沌振荡器的同步方案。首先给出了混沌耦合同步方案的数学证明，然后通过数值仿真证实了该混沌耦合同步方案的正确性和有效性。最后通过计算条件李雅谱诺夫指数，比较了不同耦合强度下，两种混沌耦合同步和典型的连续耦合同步的同步性能。计算表明在一定的耦合强度下，混沌耦合比典型的连续耦合同步速度快。     

超混沌系统的耦合同步

利用相互耦合的方法在超混沌LC振荡电路中实现了混沌同步.给出了确定耦合系数的方法,计算了最大Lyapunov指数谱,讨论并给出了耦合系数与同步时间的关系.该方法在参数不匹配情况下失去了同步. 关键词： 超混沌 混沌同步 耦合系数     

一种基于有源backstepping设计的混沌和超混沌系统的广义同步方法研究

本文提出了一种新颖的有源backstepping控制设计方法用于实现两个相同R?ssler超混沌系统的同步,并进一步将该方法推广到实现Chua混沌系统和R?ssler超混沌系统的广义同步。由于该设计方法在控制器设计的每一步中都能将Lyapunov函数的选择和有源控制器的设计紧密地结合起来考虑,从而能根据工程实际灵活地构造出合适的控制器以满足系统控制要求,同时也为控制器的设计提供了一种系统的设计方法。这正是这种设计方法的最大优点。数值结果表明了本文所提出设计方法的可行性和有效性。     

超混沌Chen系统和超混沌Roessler系统的异结构同步

用两种不同的方法——主动控制同步法和自适应控制同步法实现超混沌Chen系统和超混沌Roessler系统的异结构同步，各自设计了不同的控制器，使得响应系统与驱动系统同步．当参数已知时，采用主动控制法，方法简单有效且不需要构造Lyapunov函数，实现同步的时间短；当系统参数未知或结构不确定时，基于Lyapunov稳定性理论，给出自适应同步控制器的系统设计过程和参数自适应律，使得系统达到同步同时识别未知参数，数值模拟验证了两种方法的有效性。     

简并光学参量振荡器混沌相同步与反相同步

从广泛意义上研究了简并光学参量振荡器的混沌同步. 数值结果表明, 当最大条件李指数小于零时, 处于混沌态的两个简并光学参量振荡器通过单向耦合可以实现相同步或反相同步. 当两个简并光学参量振荡器同时实现正耦合或负耦合时为相同步, 当其中一个为正耦合而另一个为负耦合时实现反相同步.     

A novel hyperchaos evolved from three dimensional modified Lorenz chaotic system

This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the four-dimensional system can evolve into periodic, quasi-periodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.[第一段]     

Synchronization of chaos in resistive-capacitive-inductive shunted Josephson junctions

We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent （MCLE） is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.     

Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions

This paper deals with dynamical behaviours in an array composed of two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) and a shunted resistor. Numerical simulations show that periodic, chaotic and hyperchaotic states can coexist in this array. Moreover, a scheme for controlling hyperchaos in this array is presented by adjusting the external bias current. Numerical results confirm that this scheme can be effectively used to control hyperchaotic states in this array into stable periodic states, and different stable periodic states with different period numbers can be obtained by appropriately choosing the intensity of the external bias current.     

Controlling chaos in RCL-shunted Josephson junction by delayed linear feedback

The resistively-capacitively-inductively-shunted （RCL-shunted） Josephson junction （RCLSJJ） shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented based on the linear feedback theory. Numerical simulations show that this scheme can be effectively used to control chaotic states in this junction into stable periodic states. Moreover, the different stable period states with different period numbers can be obtained by appropriately adjusting the feedback intensity and delay time without any pre-knowledge of this system required.     

Controlling hyperchaos and synchronizing periodic states in the DOPO

It has been found out that hyperchaotic behaviors can be controlled to enter periodicity state by modulating the detuned parameters in degenerated optical parameter oscillator (DOPO) with different periodic orbits from different modulation index at the same modulation frequency, or from different modulation frequency at the same modulation index. It was shown that the periodic orbits of the DOPOs modulated through sinusoid can be resulted in identical synchronization or inversed synchronization only in the case that the largest Lyapunov exponent exponent of the system is negative.PACS: 42.65.Sf     

Controlling chaos in RCL-shunted Josephson junction by delayed linear feedback

The resistively--capacitively--inductively-shunted (RCL-shunted) Josephson junction (RCLSJJ) shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented based on the linear feedback theory. Numerical simulations show that this scheme can be effectively used to control chaotic states in this junction into stable periodic states. Moreover, the different stable period states with different period numbers can be obtained by appropriately adjusting the feedback intensity and delay time without any pre-knowledge of this system required.     

Generalized synchronization of chaos in erbium—doped dual—ring lasers

We investigate chaotic synchronization in the generalized sense in unidirectionally coupled erbium-doped fibre dual-ring lasers. Numerical simulation shows that no matter whether the two different erbium-doped fibre dual-ring lasers are chaotic or not before coupling, they show generalized synchronization with a suitable unidirectional coupling coefficient under which the maximum condition Lyapunov exponent is negative. We also use the auxiliary system approach to detect the generalized synchronization.