Time-delayed feedback control optimization for quasi linear systems under random excitations

A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to derive the stationary response of the system. Secondly, the control law is assumed to be velocity feedback control with time delay and the unknown control gains are determined by the performance indices. The response of the controlled system is predicted through solving the Fokker-Plank-Kolmogorov equation associated with the averaged Ito equation. Finally, numerical examples are used to illustrate the proposed control method, and the numerical results are confirmed by Monte Carlo simulation .     

Asymptotic solution for the El Nino time delay sea-air oscillator model

A sea-air oscillator model is studied using the time delay theory. The aim is to find an asymptotic solving method for the El Nino-southern oscillation （ENSO） model. Employing the perturbed method, an asymptotic solution of the corresponding problem is obtained. Thus we can obtain the prognoses of the sea surface temperature （SST） anomaly and the related physical quantities.     

High-l Rydberg States＇ Interference Using a Double-Pulse Electric Field

The interference behavior of high-1 Rydberg states is investigated in external fields. We prepare high-l states from an initial excited ns Cs Rydberg state by applying one electric-field pulse. The interference between the initial ns state and the high-I states is investigated by two time-delayed short electric-field pulses. The state selective field ionization technique is used to measure the transfer ratio versus the field pulses parameters. The visibility of interference is defined to describe interference and the results show that a relative long duration of electric-field pulse will weaken the interference.     

Time-Delay Enhanced Coherence Resonance in a Discrete Neuron with Noises

Coherence resonance in a discrete excitable neuronal model with noises and time delays is investigated. The effects of the time delays on coherence resonance are revealed in two cases： Gaussian white and Gaussian color noises, respectively. The coefficient of variation of interspike intervals is calculated by numerical simulation. The results show that the coherence resonance is enhanced with the time delay increasing in the weak noises intensity cases, while there is no effect in the large noise intensity. Moreover, the coherence resonance can be held back by the self-correlation time, when the system is driven by a color noise.     

TDI CCD成像电路系统响应模型的研究

为建立准确的时间延迟积分电荷耦合元件(TDI CCD)成像电路系统的响应模型,根据成像系统的信号处理流程,详细分析了CCD传感器、预放电路与视频处理电路等主要环节对系统响应的影响,并结合理论响应模型,针对实际的处理流程,建立了实际系统的理论响应模型。利用某航天相机TDI CCD成像系统进行了暗电流噪声、视频处理电路噪声等专项测试实验,并在不同的拍照参数与光辐射条件下进行了辐射定标实验,分析了具体的实验图像数据,采用最小二乘法的线性拟合与二次多项式拟合分别得到了系统响应的近似数学模型和高精度数学模型,拟合决定系数R2分别达到了0.992和0.9998。利用该响应模型可以准确计算卫星在轨拍照时地物的辐射特性,并为合理选择相机在轨拍照参数提供依据。成像实验表明,系统响应模型准确,参数设置合理,满足相机在轨拍照的任务要求,提高了相机在轨工作的效率。     

用时间延迟方法压低喇曼增强非简并四波混频谱的热背底

证明了使用时延方法可再现淹没在热背底中的喇曼信号，并且喇曼增强非简并四波混频光谱恢复为通常煌带有源于分子取向栅非共振背底的非对称线型，实验结果与理论予示一致。     

用双光源相位共轭型非相干光时间延迟简并四波混频测量超快速过程

本文提出用双光源相位共轭型非相干光时间延迟简并四波混频测量失相时间和布居弛豫时间的理论,并对其应用进行了讨论.     

Stability and Neimark-Sacker bifurcation analysis of a food-limited population model with a time delay

In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the linear stability of this model is studied.It is shown that Neimark-Sacker bifurcation occurs when τ crosses certain critical values.The explicit formulae which determine the stability,direction,and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form.Finally,numerical simulations are performed to verify the analytical results.     

Stability and Hopf bifurcation of a delayed ratio-dependent predator-prey system

Since the ratio-dependent theory reflects the fact that predators must share and compete for food, it is suitable for describing the relationship between predators and their preys and has recently become a very important theory put forward by biologists. In order to investigate the dynamical relationship between predators and their preys, a so-called Michaelis-Menten ratio-dependent predator-prey model is studied in this paper with gestation time delays of predators and preys taken into consideration. The stability of the positive equilibrium is investigated by the Nyquist criteria, and the existence of the local Hopf bifurcation is analyzed by employing the theory of Hopf bifurcation. By means of the center manifold and the normal form theories, explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. The above theoretical results are validated by numerical simulations with the help of dynamical software WinPP. The results show that if both the gestation delays are small enough, their sizes will keep stable in the long run, but if the gestation delays of predators are big enough, their sizes will periodically fluc-tuate in the long term. In order to reveal the effects of time delays on the ratio-dependent predator-prey model, a ratiodependent predator-prey model without time delays is considered. By Hurwitz criteria, the local stability of positive equilibrium of this model is investigated. The conditions under which the positive equilibrium is locally asymptotically stable are obtained. By comparing the results with those of the model with time delays, it shows that the dynamical behaviors of ratio-dependent predator-prey model with time delays are more complicated. Under the same conditions, namely, with the same parameters, the stability of positive equilibrium of ratio-dependent predator-prey model would change due to the introduction of gestation time delays for predators and preys. Moreover, with the variation of time delays, the positive equilibrium of the ratio-dependent predator-prey model subjects to Hopf bifurcation.     

Uniformly ultimate boundedness for discontinuous systems with time-delay

The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed. Based on the Lyapunov-Krasovskii functional, the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented. Furthermore, the result is applied to a class of mechanical systems with a retarded discontinuous friction item.