基于Chebyshev多项式逼近的随机 van der Pol系统的倍周期分岔分析

应用 Chebyshev 多项式逼近法研究了谐和激励作用下具有随机参数的随机van der Pol系统 的倍周期分岔现象.随机系统首先被转化成等价的确定性系统，然后通过数值方法求得响应 ，借此探索了随机van der Pol系统丰富的随机倍周期分岔现象.数值模拟显示随机van der Pol 系统存在与确定性系统极为相似的倍周期分岔行为，但受随机因素的影响，又有与之不 同之处.数值结果表明，Chebyshev 多项式逼近是研究非线性系统动力学问题的一种新的有 效方法. 关键词： Chebyshev 多项式 随机van der Pol 系统 倍周期分岔     

Analysis of stochastic bifurcation and chaos in stochastic Duffing--van der Pol system via Chebyshev polynomial approximation

The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing--van der Pol system with bounded random parameter of exponential probability density function subjected to a harmonic excitation. Firstly the stochastic system is reduced into its equivalent deterministic one, and then the responses of stochastic system can be obtained by numerical methods. Nonlinear dynamical behaviour related to stochastic period-doubling bifurcation and chaos in the stochastic system is explored. Numerical simulations show that similar to its counterpart in deterministic nonlinear system of stochastic period-doubling bifurcation and chaos may occur in the stochastic Duffing--van der Pol system even for weak intensity of random parameter. Simply increasing the intensity of the random parameter may result in the period-doubling bifurcation which is absent from the deterministic system.     

含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔

讨论简谐激励作用下含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔现象.首先用Chebyshev 多项式逼近法将随机Duffing-van der Pol系统化成与其等价的确定性系统，然后通过等价确定性系统来探索该系统的倍周期分岔现象.数值模拟显示随机Duffing-van der Pol 系统与均值参数系统有着类似的倍周期分岔行为，同时指出，随机参数系统的倍周期分岔有其自身独有的特点.文中的主要数值结果表明Chebyshev 多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法. 关键词： Chebyshev多项式 随机Duffing-van der Pol系统 倍周期分岔     

Stochastic period-doubling bifurcation analysis of a Rssler system with a bounded random parameter

This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rssler system with an arch-like bounded random parameter. First, we transform the stochastic Rssler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic Rssler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Rssler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rssler system.     

Stochastic period-doubling bifurcation in biharmonic driven Dulling system with random parameter

Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations.     

一类随机van der Pol系统的Hopf 分岔研究

研究了一类随机van der Pol 系统的Hopf分岔行为.首先根据Hilbert空间的正交展开理论,含有随机参数的van der Pol系统被约化为等价确定性系统,然后利用确定性分岔理论分析了等价系统的Hopf分岔,得出了随机van der Pol 系统的Hopf 分岔临界点,探究了随机参数对系统Hopf分岔的影响.最后利用数值模拟验证了理论分析结果. 关键词： 随机van der Pol系统 Hopf分岔 正交多项式逼近     

随机Bonhoeffer-Van der Pol系统的随机混沌控制

讨论了具有有界随机参数的随机Bonhoeffer-Van der Pol系统的随机混沌现象，并利用噪声对其进行控制.首先运用Chebyshev多项式逼近的方法，将随机Bonhoeffer-Van der Pol系统转化为等价的确定性系统，使原系统的随机混沌控制问题转换为等价的确定性系统的确定性混沌控制问题，继而可用Lyapunov指数指标来研究等价确定性系统的确定性混沌现象和控制问题.数值结果表明，随机Bonhoeffer-Van der Pol系统的随机混沌现象与相应的确定性Bonhoeffer-Van der Pol系统极为相似.利用噪声控制法可将混沌控制到周期轨道，但是在随机参数及其强度的影响下也呈现出一些特点.     

双边约束条件下随机van der Pol系统的分岔研究

利用随机光滑动力系统的Chebyshev正交多项式逼近方法,研究了双边约束条件下随机van der Pol系统的分岔现象.数值研究表明,双边约束随机van der Pol系统中不仅存在着丰富的倍周期分岔现象,还存在非光滑系统中所特有的擦边分岔.着重研究了随机非光滑系统中的擦边分岔,分析了随机因素对非光滑动力系统中擦边分岔的影响.研究表明,Chebyshev多项式逼近也是研究随机非光滑系统动力学行为的一种有效方法. 关键词： 非光滑动力系统 随机 van der Pol系统 擦边分岔 双边约束     

随机Duffing单边约束系统的倍周期分岔

通过引进平均约束面和平均跃变方程对随机约束系统的约束条件进行处理，把研究随机光滑系统倍周期分岔的Chebyshev多项式逼近的方法运用到随机非光滑系统中，数值研究表明随机Duffing单边约束系统同样存在丰富的倍周期分岔现象，Chebyshev多项式逼近是研究带有约束的随机非光滑动力系统的有效方法. 关键词： 非光滑动力系统 随机Duffing系统 Chebyshev多项式 倍周期分岔     

Orientation-enhanced nonlinear optical properties and phase-conjugate reflective system of a novel Azobenzene doped polymer film

This paper reports that the nonlinear refractive index of a novel organic optical storage film doped azo-diphenylamine polymer is measured by using the $Z$-scan technique. The nonlinear refractive index up to $3.7\times 10 ^{ - 6 }$~cm$^{2}$/W induced by thermo-optical effect is obtained. It indicates that the sample has excellent optical nonlinear properties. The physical mechanism of the great nonlinear optical effect is analysed and the optical conjugate characteristic is also discussed with degenerate four-wave-mixing. The phase conjugate wave diffracted from the formative refractive index grating in the sample is acquired and its equivalent reflectivity reaches about 22{\%}. On this basis, the reflective wave phase-conjugated mirror system was designed, and the image aberration experienced in propagation in the storage experiment is corrected by using the system.     

Stochastic period-doubling bifurcation analysis of a R?ssler system with a bounded random parameter

This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional R?ssler system with an arch-like bounded random parameter. First, we transform the stochastic R?ssler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic R?ssler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic R?ssler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic R?ssler system.     

Duffing-van der Pol振子随机分岔的全局分析

应用广义胞映射方法研究了参激和外激共同作用的Duffing-van der Pol振子的随机分岔.以 系统参数通过某一临界值时，如果系统的随机吸引子或随机鞍的形态发生突然变化，则认为 系统发生随机分岔为定义，分析了参激强度和外激强度的变化对于随机分岔的影响.揭示了 随机分岔的发生主要是由于系统的随机吸引子与系统的随机鞍碰撞产生的.分析表明，广义 胞映射方法是分析随机分岔的有力工具，这种全局分析方法可以清晰地给出随机分岔的发生 和发展. 关键词： 随机分岔 全局分析 广义胞映射方法 随机吸引子 随机鞍     

Surface second harmonic generation of chiral molecules using three-coupled-oscillator model

Based on the three-coupled-oscillator molecular model we proposed, the relation between the second-order susceptibilities of a chiral film and the molecular hyperpolarizabilities is given. The effect of microscopic parameters on the second-order susceptibilities is simulated numerically and the difference between the efficiencies of s-polarized second-harmonic fields induced by the left- and the right-handed circularly-polarized fundamental beams is discussed. The theoretical basis for studying second-order nonlinear optical properties of the chiral molecular media with a tripod-like structure is provided in this paper.     

Growth parameter dependence of magnetic property of CrAs thin film

This paper has systematically investigated the substrate temperature and thickness dependence of surface morphology and magnetic property of CrAs compound films grown on GaAs by molecular-beam epitaxy. It finds that the substrate temperature affects the surface morphology and magnetic property of CrAs thin film more potently than the thickness.     

The effect of electronic orbital interactions on p-type doping tendency in ZnO series： First-principles calculations

The electronic structures and optical properties of B3 ZnO series of Znelectronic structures, optical properties, pseudopotential plane-wave method, \\ \hspace*{1.9cm} p-type doping tendency,electronic structures, optical properties, pseudopotential plane-wave method, \\ \hspace*{1.9cm} p-type doping tendencyProject supported by the National Natural Science Foundation of China (Grant No~10625416).2007-04-252007-06-18The electronic structures and optical properties of B3 ZnO series of Zn4X4-yMy（X ：O, S, Se or Te; M = N, Sb, C1 or I; y = 0 or 1） are studied by first-principles calculations using a pseudopotential plane-wave method. The results show that Zn d-X p orbital interactions play an important role in the p-type doping tendency in zinc-based Ⅱ-Ⅵ semiconductors. In ZnX, with increasing atomic number of X, Zn d-X p orbital interactions decrease and Zn s-X p orbital interactions increase. Additionally, substituting group-V elements for X will reduce the Zn d-X p orbital interactions while substituting group-VII elements for X will increase the Zn d-X p orbital interactions. The results also show that group-V-doped ZnX and group-Ⅷ-doped ZnX exhibit different optical behaviours due to their different orbital interaction effects.     

Preparation and tribological properties of DLC/Ti filmby pulsed laser arc deposition

This paper reports that DLC (diamond like carbon)/Ti and DLC films were prepared by using pulsed laser arc deposition. R-ray diffraction, Auger electron spectroscopy, Raman spectroscopy, atomic force microscopy, nanoindenter, spectroscopic ellipsometer, surface profiler and micro-tribometer were employed to study the structure and tribological properties of DLC/Ti and DLC films. The results show that DLC/Ti film, with $I(D)/I(G)$ 0.28 and corresponding to 76{\%} sp$^{3}$ content calculated by Raman spectroscopy, uniform chemical composition along depth direction, 98 at{\%} content of carbon, hardness 8.2 GPa and Young's modulus 110.5 GPa, compressive stress 6.579 GPa, thickness 46~nm, coefficient of friction 0.08, and critical load 95mN, exhibits excellent mechanical and tribological properties.     

Effects of South China Sea/western North Pacific summer monsoon on tropospheric biennial oscillation （TBO）

Several theories have been developed to explain tropical biennial oscillation (TBO), as an air--sea interactive system to impact Asian and global weather and climate, and some models have been established to produce a TBO. A simple 5-box model, with almost all the key processes associated with TBO, can produce a TBO by including air--sea interactions in the monsoon regions. Despite that, the South China Sea/western North Pacific summer monsoon (SCS/WNPSM), a very important monsoon subsystem, is neglected. In this paper, based on the dynamical framework of 5-box model, the term of SCS/WNPSM has been added and a 6-box model has been developed. Comparing the difference of TBO sensibilities with several key parameters, air--sea coupling coefficient α, SST-thermocline feedback coefficient γ and wind-evaporation feedback coefficient λ, between the modified model and original model, TBO is more sensible to the parameters in the new model. The results imply that the eastern Pacific and local wind-evaporation play more important roles in the TBO when including SCS/WNPSM.     

Vertical profiles of aerodynamic size distribution for airborne particles over Yangtze River Delta

Based on the aircraft observations in the summer of 2003, we have studied the aerodynamic size distributions of airborne particles at altitudes ranging from 400 m to 2800 m over the central and southern areas of Jiangsu province located in Yangtse River Delta of China. The sizes of airborne particles are measured to be in a range of 0.47- 30 μm with 57 channels, and their number concentrations, surface area concentrations and mass concentrations are also measured. The results show that the concentrations of airborne particles are very low above an altitude of 2000 m and the size distributions present a specific multi-peak mode by using insufficient samples. Below 1000 m, however, the concentrations of particles increase obviously, and their size distribution is similar to that at the ground level. The study also indicates that the concentrations, size distributions and median diameters of airborne particles above and below the boundary layer are very different, displaying different pollution features. Meanwhile, the results also show that the pollution level of airborne particles has a descending tendency with altitude increasing.     

Stochastic response of van der Pol oscillator with two kinds of fractional derivatives under Gaussian white noise excitation

This paper aims to investigate the stochastic response of the van der Pol(VDP) oscillator with two kinds of fractional derivatives under Gaussian white noise excitation.First,the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique.Then,the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution.Finally,the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator.The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order,the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator.An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary.     

Self-consistent analysis of double-δ-doped InAlAs/InGaAs/InP HEMTs

We have carried out a theoretical study of double-5-doped InAlAs/InGaAs/InP high electron mobility transistor （HEMT） by means of the finite differential method. The electronic states in the quantum well of the HEMT are calculated self-consistently. Instead of boundary conditions, initial conditions are used to solve the Poisson equation. The concentration of two-dimensional electron gas （2DEG） and its distribution in the HEMT have been obtained. By changing the doping density of upper and lower impurity layers we find that the 2DEG concentration confined in the channel is greatly affected by these two doping layers. But the electrons depleted by the Schottky contact are hardly affected by the lower impurity layer. It is only related to the doping density of upper impurity layer. This means that we can deal with the doping concentrations of the two impurity layers and optimize them separately. Considering the sheet concentration and the mobility of the electrons in the channel, the optimized doping densities are found to be 5 × 10^12 and 3× 10^12 cm^-2 for the upper and lower impurity layers, respectively, in the double-5-doped InAlAs/InGaAs/InP HEMTs.