一类时滞递归神经网络模型的周期振动性

利用线性矩阵不等式方法,研究一类5个神经元时滞递归神经网络模型的周期振动性,得出保证系统存在周期振动性的一组充分条件,理论分析和数值仿真显示,所得结果为一类5个神经元时滞递归神经网络模型提供了新的振动性判定准则。

Oscillation of Neutral Differential_difference Equations with Positive and Negative Periodic Coefficients

Some sufficient conditions are obtained for the oscillation of first order neutral differential_difference equations with positive and negative periodic coefficients.

Quadratic integrability of solutions based on a class of delayed systems

Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function, the Lyapunov functional or the Beuman-Bihari inequality, and some sufficient conditions based on those properties are given. Finally, the conclusions are applied to over-voltage models based on three-phase nonsynchronous closing of switches appearing in the power systems, the results in accord with the background physical meaning are obtained. And all the conditions of the conclusions are easy to validate, so the conclusions have definite theoretical meaning and are easy to apply in practice.

CALCULATING ACCURATE PERIODIC MOTIONS OF HARMONICALLY FORCED PIECEWISE LINEAR OSCILLATORS

This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the traditional numerical Poincare mapping and its Jacobian replaced by the piecewise analytic ones. Thus, the scheme gets rid of the requirement of the current schemes for an assumed order of the oscillator trajectory passing through different linear regions. The numerical examples in the paper demonstrate that the new scheme, compared with the current schemes, enables one to cope with more complicated dynamics of harmonically forced piecewise linear oscillators.

Stability of columns with original defects under periodic transient loadings

To study the influence of original defects on the dynamic stability of the columns under periodic transient loadings,the approximate solution method and the Fourier method of the stable periodic solution are adopted while considering the influence of original defects on columns.The dynamic stability of the columns under periodic transient loadings is analyzed theoretically.Through the study of different deflections,the dynamic instability of the columns is obtained by Maple software.The results of theoretical analysis show that the larger the original defects,the greater the unstable area,the stable solution amplitude of columns and the risk of instability caused by parametric resonance will be.The damping of columns is a vital factor in reducing dynamic instability at the same original defects.On the basis of the Mathieu-Hill equation,the relationship between the original defects and deflection is deduced,and the dynamic instability region of the columns under different original defects is obtained.Therefore,reducing the original defects of columns can further enhance the dynamic stability of the compressed columns in practical engineering.

Analysis of the Mode of the Periodically Time-varying Vibration Systems

By Liapunov reducibility theorem, the periodically time-varying vibration system can be transformed to a linear time-invariant system. Based on the dynamic characteristics of the linear time-invariant system, the mode of the periodically time-varying vibration system has been discussed. The paper defines the mode and analyzes its characteristics. It can be found that the mode of the periodically time-varying system is periodically time-varing but has such characteristics as orthogonality. Finally, a method is given to solve the mode. By solving the eigenvalues and the eigenvectors of the state transition matrix in one period, the periodically time-varying mode can be obtained.

The relationship between intermittent limit cycles and postural instability associated with Parkinson’s disease

Background:Many disease-specific factors such as muscular weakness,increased muscle stiffness,varying postural strategies,and changes in postural reflexes have been shown to lead to postural instability and fall risk in people with Parkinson's disease(PD).Recently,analytical techniques,inspired by the dynamical systems perspective on movement control and coordination,have been used to examine the mechanisms underlying the dynamics of postural declines and the emergence of postural instabilities in people with PD.Methods:A wavelet-based technique was used to identify limit cycle oscillations(LCOs) in the anterior–posterior(AP) postural sway of people with mild PD(n = 10) compared to age-matched controls(n = 10).Participants stood on a foam and on a rigid surface while completing a dual task(speaking).Results:There was no significant difference in the root mean square of center of pressure between groups.Three out of 10 participants with PD demonstrated LCOs on the foam surface,while none in the control group demonstrated LCOs.An inverted pendulum model of bipedal stance was used to demonstrate that LCOs occur due to disease-specific changes associated with PD:time-delay and neuromuscular feedback gain.Conclusion:Overall,the LCO analysis and mathematical model appear to capture the subtle postural instabilities associated with mild PD.In addition,these findings provide insights into the mechanisms that lead to the emergence of unstable posture in patients with PD.

Stationary and Non-stationary Self-Induced Vibrations in Waveguiding Systems

With the use of a wave model, the non-linear problem about realization of the Poincare-Hopf bifurcations in waveguiding systems is stated. The constitutive non-linear differential equations are deduced, the methods for their solution are elaborated. The example of torsion wave propagation in an elongated drill string is considered. Computer simulation of auto-oscillation generation in the examined system is performed for the cases of stationary and non-stationary variations of the perturbation parameter. The diapason of the drilling rotation velocity values corresponding to regimes of stable self-excited periodic motions of the system is found. This domain is shown to be limited by the states of the Poincare-Hopf bifurcations. Owing to the feature that the stated problem is singularly perturbed, the autovibrations are of relaxation type with fast and slow motions. Influence of the length of the uniform and articulated drill strings on the bifurcation values of their angular velocities of generation and accomplishment of the auto-oscillation processes in the drill strings is discussed.

Simulation of shock wave buffet and its suppression on an OAT15A supercritical airfoil by IDDES

In the present paper,extremely unsteady shock wave buffet induced by strong shock wave/boundary-layer interactions (SWBLI) on the upper surface of an OAT15A supercritical airfoil at Mach number of 0.73 and angle of attack of 3.5 degrees is first numerically simulated by IDDES,one of the most advanced RANS/LES hybrid methods.The results imply that conventional URANS methods are unable to effectively predict the buffet phenomenon on the wing surface;IDDES,which involves more flow physics,predicted buffet phenomenon.Some complex flow phenomena are predicted and demonstrated,such as periodical oscillations of shock wave in the streamwise direction,strong shear layer detached from the shock wave due to SWBLI and plenty of small scale structures broken down by the shear layer instability and in the wake.The root mean square (RMS) of fluctuating pressure coefficients and streamwise range of shock wave oscillation reasonably agree with experimental data.Then,two vortex generators (VG) both with an inclination angle of 30 degrees to the main flow directions are mounted in front of the shock wave region on the upper surface to suppress shock wave buffet.The results show that shock wave buffet can be significantly suppressed by VGs,the RMS level of pressure in the buffet region is effectively reduced,and averaged shock wave position is obviously pushed downstream,resulting in increased total lift.

Area spectra of BTZ black holes via periodicity

Motivated by the recent work that the periodicity of a black hole is responsible for the area spectrum,we exclusively utilize the period of motion of an outgoing wave,which is shown to be related to the vibrational frequency of the perturbed black hole,to study area spectra of a non-rotating BTZ black hole and a rotating BTZ black hole.It is found that the area spectra and entropy spectra for both space times are equally spaced.In addition,we find that though the entropy spectra of the 3-dimensional BTZ black holes take the same form as those of the 4-dimensional black holes,the area spectra depend on the dimension of space times.Our result confirms that the entropy spectrum of a black hole is more fundamental than the area spectrum.

Ionospheric absorption and planetary wave activity in East Asia sector

In this paper, we focus on ionospheric absorption in the East Asia sector, and look for manifestations of atmospheric influences in this area. First, a 4-year historical record of absorption measurement at Beijing is presented. This record was obtained by a sweep frequency technique, in which 27-days periodic variation of the absorption level was found to be dominant, appearing in most seasons except winters. Instead, unusual enhancements of the absorption level appeared in winters (winter anomaly), at the meantime the level varied with periods mainly in the range of 8-12 days. Comparing to 27-days period from the Sun, the shorter period oscillations should be related to planetary wave activities in lower atmosphere. Second, fmin data from 5 mid-latitude ionosondes in Japan were used as an indirect but long-term measurement. With the fmin data covering two solar cycles, disturbances with various periods were found to be active around solar maximum years, but the 8-12 days oscillations always existed in winter, showing seasonal dependence instead of connection to solar activity. These results given in this paper demonstrate seasonal and solar cycle-dependent features of the ionospheric absorption in East Asia sector, and confirm the existence of influence from atmosphere-ionosphere coupling in this area, as well as the relationship between ionospheric winter anomaly and planetary wave activity.

A MAPLE PACKAGE OF AUTOMATED DERIVATION OF HOMOTOPY ANALYSIS SOLUTION FOR PERIODIC NONLINEAR OSCILLATIONS

Based on the homotopy analysis method, a general analytic technique for strongly nonlinear problems, a Maple package of automated derivation （ADHO） for periodic nonlinear oscillation systems is presented. This Maple package is valid for periodic oscillation systems in rather general, and can automatically deliver the accurate approximations of the frequency co and the mean of motion δof a nonlinear periodic oscillator. Based on the homotopy analysis method which is valid even for highly nonlinear problems, this Maple package can give accurate approximate expressions even for nonlinear oscillation systems with strong nonlinearity. Besides, the package is user-friendly： One just needs to input a governing equation and initial conditions, and then gets satisfied analytic approximations in few seconds. Several different types of examples are given in this paper to illustrate the validity of this Maple package. Such kind of package provides us a helpful and easy-to-use tool in science and engineering to analyze periodic of this Maple package from the is published publicly. nonlinear oscillations. And it is free address http：//numericaltank.sjtu to download the electronic version edu.cn/sjliao.htm once the paper