Chaotic state as an output of vacuum state evolving in diffusion channel and generation of displaced chaotic state for quantum controlling

We show that chaotic state can be produced as an output of vacuum state evolving in diffusion channel,while displaced chaotic state is output of a coherent state evolving in diffusion channel.We also introduce the thermo vaccum state for the displaced chaotic state and evaluate the average photon number.The displaced chaotic state may be used exhibiting quantum controlling.

Number-chaotic State光场与原子相互作用耦合系统中的量子关联

在强度关联耦合(IDC)条件下,对单模Number-chaotic State光场与两个二能级原子相互作用系统中的纠缠与量子关联动力学演化特性进行了探究。着重研究了多光子跃迁和强度耦合参数对纠缠与量子关联特性的影响。结果表明,当量子纠缠为零时,原子间仍然存在着一定的量子关联效应。随光场光子数的增大,纠缠与量子关联演化的周期均变短,光子跃迁数增大将使得量子纠缠与量子关联的演化呈现无规振荡形式。

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features：（i） it enables synchronization to be achieved for both cases of n 〈 m and n 〉 m;（ii） it is rigorous,being based on theorems;（iii） it can be readily applied to any chaotic（hyperchaotic） maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map（as the drive system） and the three-dimensional hyperchaotic Wang map（as the response system）,and the three-dimensional H′enon-like map（as the drive system） and the two-dimensional Lorenz discrete-time system（as the response system）.

An observer based asymptotic trajectory control using a scalar state for chaotic systems

A state-observer based full-state asymptotic trajectory control （OFSTC） method requiring a scalar state is presented to asymptotically drive all the states of chaotic systems to arbitrary desired trajectories. It is no surprise that OFSTC can obtain good tracking performance as desired due to using a state-observer. Significantly OFSTC requires only a scalar state of chaotic systems. A sinusoidal wave and two chaotic variables were taken as illustrative tracking trajectories to validate that using OFSTC can make all the states of a unified chaotic system track the desired trajectories with high tracking accuracy and in a finite time. It is noted that this is the first time that the state-observer of chaotic systems is designed on the basis of Kharitonov＇s Theorem.

Time evolution of a squeezed chaotic field in an amplitude damping channel when used as a generating field for a squeezed number state

We investigate how an optical squeezed chaotic field（SCF） evolves in an amplitude dissipation channel. We have used the integration within ordered product of operators technique to derive its evolution law. We also show that the density operator of SCF can be viewed as a generating field of the squeezed number state.

A specific state variable for a class of 3D continuous fractional-order chaotic systems

A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable and its （q-order and 2q-order） time derivatives. This idea is demonstrated by using several well-known fractional-order chaotic systems. Finally, a synchronization scheme is investigated for this fractional-order chaotic system via a specific state variable and its （q-order and 2q-order） time derivatives. Some examples are used to illustrate the effectiveness of the proposed synchronization method.

THE STATE SPACE RECONSTRUCTION TECHNOLOGY OF DIFFERENT KINDS OF CHAOTIC DATA OBTAINED FROM DYNAMICAL SYSTEM

Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different kinds of chaotic data obtained from dynamical system has also been discussed in detail.

Thermal vacuum state corresponding to squeezed chaotic light and its application

For the density operator（mixed state） describing squeezed chaotic light（SCL） we search for its thermal vacuum state（a pure state） in the real-fictitious space. Using the method of integration within ordered product（IWOP） of operators we find that it is a kind of one- and two-mode combinatorial squeezed state. Its application in evaluating the quantum fluctuation of photon number reveals： the stronger the squeezing is, the larger a fluctuation appears. The second-order degree of coherence of SCL is also deduced which shows that SCL is classic. The new thermal vacuum state also helps to derive the Wigner function of SCL.

Predicting of Power Quality Steady State Index Based on Chaotic Theory Using Least Squares Support Vector Machine

An effective power quality prediction for regional power grid can provide valuable references and contribute to the discovering and solving of power quality problems. So a predicting model for power quality steady state index based on chaotic theory and least squares support vector machine (LSSVM) is proposed in this paper. At first, the phase space reconstruction of original power quality data is performed to form a new data space containing the attractor. The new data space is used as training samples for the LSSVM. Then in order to predict power quality steady state index accurately, the particle swarm algorithm is adopted to optimize parameters of the LSSVM model. According to the simulation results based on power quality data measured in a certain distribution network, the model applies to several indexes with higher forecasting accuracy and strong practicability.

三阶三次幂非线性混沌电路的自适应反馈控制和H_(∞)控制

针对三阶三次幂非线性混沌电路,研究其控制问题.首先,给出系统的Lyapunov指数和混沌吸引子,验证系统存在复杂的混沌现象;其次,用自适应反馈控制方法和H_(∞)状态反馈控制方法,设计参数已知和参数未知的自适应反馈控制器以及H_(∞)状态反馈控制器,将混沌系统状态稳定到平衡点上;最后,通过MATLAB软件进行数值仿真验证控制器的有效性,并对两种控制器的控制效果进行比较.

Arbitrary full-state hybrid projective synchronization for chaotic discrete-time systems via a scalar signal

In this paper we present a new projective synchronization scheme, where two chaotic （hyperchaotic） discrete-time systems synchronize for any arbitrary scaling matrix. Specifically, each drive system state synchronizes with a linear combination of response system states. The proposed observer-based approach presents some useful features： i） it enables exact synchronization to be achieved in finite time （i.e., dead-beat synchronization）; ii） it exploits a scalar synchronizing signal; iii） it can be applied to a wide class of discrete-time chaotic （hyperchaotic） systems; iv） it includes, as a particular case, most of the synchronization types defined so far. An example is reported, which shows in detail that exact synchronization is effectively achieved in finite time, using a scalar synchronizing signal only, for any arbitrary scaling matrix.

PMSM混沌系统无初始状态约束的固定时间有界控制

永磁同步电机(PMSM)是一种多变量、耦合性强的非线性系统,在实际运行过程中会出现混沌振荡。为了抑制PMSM系统的混沌,本文设计一种无初始状态约束的固定时间有界控制器。首先根据PMSM系统各个子系统的虚拟误差设计虚拟控制器,通过反步法推导得出控制器具有较高的抗干扰性能和鲁棒性,并证明时变反馈参数能够保证系统在到达有限时间收敛的同时达到渐近稳定,且稳定时间只与规定的边界有关。最后数值仿真通过调整控制系数k使系统能够在不同的初始状态下快速达到稳定,验证了所设计的控制器无论系统的初始状态如何,都能够使系统在2.8 s内达到稳定状态且输出收敛于给定的边界。

Master equation describing the diffusion process for a coherent state

The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state＇s evolution during the diffusion process, fully utilizing the technique of integration within an ordered product （IWOP） of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dp/dt = -κ[a＋ap -a＋pa -apa＋ ＋ paa＋]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.

双参保守复混沌系统的构建及偏置增压控制

基于经典保守混沌系统的结构,构造了一个双参数保守混沌系统,能够产生复杂动力学现象。通过理论分析和多种数值仿真方法,研究了系统结构参数和外力参数对混沌性、保守性、平衡状态和稳定性的影响。结果表明,随着参数的变化,系统相体积保持守恒,呈现混沌、周期运动等现象,并证明了参数对平衡状态的影响。此外,通过虚实分离的方法构造了复系统,并研究了其动力学特性,发现实混沌系统所构造的复系统中,同样具有混沌性和保守性,且具有大参数范围混沌现象。设计了控制器,使系统产生偏置增压现象,并可对信号极性进行控制。最后,设计了系统电路并进行了仿真,结果与理论相符,证明了混沌系统的物理可行性。

一个新四维混沌系统的状态观测器同步

为促进结构简单型混沌系统在工程上的应用,提出一个新的仅有一项二次非线性项的四维混沌系统.对提出的新系统的动力学性质进行理论分析,并通过MATLAB工具绘制出新系统的吸引子图和Lyapunov指数图等.仿真结果验证了系统的混沌特性.选用状态观测器对新混沌系统进行同步设计,再通过MATLAB软件数值仿真,对生成的误差图像进行实验观测,获得了良好的实验结果,也证实了该同步方法的可行性.

延迟回声状态神经网络用于复杂系统分析和应用

提出一种改进的回声状态神经网络模型,用于复杂系统的长期行为分析和预测.模型通过引入隐层状态的延迟反馈体现系统过去时刻的信息对当前状态的影响,避免了传统回声状态网络方法记忆能力弱的缺点以及获得最优参数的困难.

The improved local linear prediction of chaotic time series

Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.

PC synchronization of a class of chaotic systems via event-triggered control

The PC synchronization of a class of chaotic systems is investigated in this paper. The drive system is assumed to have only one state variable available. By constructing proper observers, some novel criteria for PC synchronization are proposed via event-triggered control scheme. The Lii system and Chen system are taken as examples to demonstrate the efficiency of the proposed approach.

Observer of a class of chaotic systems:An application to Hindmarsh–Rose neuronal model

This paper first investigates the observer of a class of chaotic systems, and then discusses the synchronization between two identical Hindmarsh–Rose（HR） neuronal chaotic systems. Both the drive and response systems are assumed to have only one state variable available. By constructing proper observers, some novel criteria for synchronization are proposed via a scalar input. Numerical simulations are given to demonstrate the efficiency of the proposed approach.

The feedback control of fractional order unified chaotic system

This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.