On stability of nonlinear continuous-time neural networks with delays

We utilize the Lyapunov function method to analyze stability of continuous nonlinear neural networks with delays and obtain some new sufficient conditions ensuring the globally asymptotic stability independent of delays. Three main conditions imposed on the weighting matrices are established. (i). The spectral radius ρ(M⁻¹(|W⁰|+|W^τ|)K)<1. (ii). The row norm M⁻¹(|W⁰|+|W^τ|)K+P⁻¹((|W⁰|+|W^τ|)KM⁻¹)^TP_∞<2. (iii). μ₂(W⁰)+W^τ_2,F<(m/k). These three conditions are independent to each other. The delayed Hopfield network, Bidirectional associative memory network and cellular neural network are special cases of the network model considered in this paper. So we improve some previous works of other researchers.     

Improvement of motor functions by noisy vestibular stimulation in central neurodegenerative disorders

Through the cerebellar vermis, the vestibular nerves are known to influence the basal ganglia and the limbic system. By means of noisy galvanic vestibular stimulation (GVS), it may be possible to ameliorate movement disorders, particularly akinesic symptoms, in patients with central neurodegenerative disorders. We evaluated the effect of 24-hour noisy GVS on a power-law temporal autocorrelation exponent of daytime wrist activity, separately for higher (local maxima) and lower (local minima) levels of activity, in 14 hospitalized patients. The power-law exponent for the local maxima was significantly (p < 0.002) lower with the noisy GVS than with sham stimulation, suggestive of more frequent switching behavior from low to high levels of activity or less severe akinesia. The noisy GVS may thus potentially improve certain motor dysfunctions in patients with distinct central neurodegenerative diseases.     

心电QRS积分信号的非线性分析

QRS波群积分能反映心室去极化活动,为不少心电研究者所重视。本文采用了非线性的分析方法,在非线性去噪的基础上重构此积分信号的相空间,计算了吸引子的相关维数与最大L yapunov指数值,分析了QRS波群积分的混沌特征。利用MIT- BIH心电数据库数据分析了多种情况下QRS波群积分的非线性指标变化特点,并同HRV信号非线性分析相比较,发现在某些情况下对QRS波群积分序列分析更具有优势。结论是利用QRS波群积分信号的非线性指标可对心脏功能做出评价。     

New conditions for global exponential stability of cellular neural networks with delays

In this paper, we study further a class of cellular neural networks model with delays. By employing the inequality , constructing a new Lyapunov functional, and applying the Homeomorphism theory, we derive some new conditions ensuring the existence, uniqueness of the equilibrium point and its global exponential stability for cellular neural networks. These conditions are independent of delays and posses infinitely adjustable real parameters, which are of highly important significance in the designs and applications of networks. In addition, we extend or improve the previously known results.     

Nonlinear analysis of posturographic data

The aim of this work is to determine whether postural sway can be well described by nonlinear deterministic modelling. Since the results of nonlinear analysis depend on experimental data processing, emphasis was given to the assessment of a proper methodology to process posturographic data. Centre of Pressure (CoP) anterior-posterior (AP) displacements (stabilogram) were obtained by static posturography tests performed on control subjects. A nonlinear determinism test was applied to investigate the nature of data. A nonlinear filtering method allowed us to estimate properly the parameters of the nonlinear model without altering signal dynamics. The largest Lyapunov exponent (LLE) was estimated to quantify the chaotic behaviour of postural sway. LLE values were found to be positive although close to zero. This suggests that postural sway derives from a process exhibiting weakly chaotic dynamics.     

Chaotic and phase-locked responses of the somatosensory cortex to a periodic medial lemniscus stimulation in the anesthetized rat

Field potential responses of the somatosensory cortex to a periodic medial lemniscus (ML) fiber stimulation were investigated in anesthetized rats. Since the field potential responses of the cortex depend on the depth of anesthesia, two criteria were introduced to control the depth of anesthesia. One criterion is that spindle oscillations are caused by a single shock to ML fibers, and the other is that the dominant frequency of spontaneous field potential rhythm is in the frequency range of the delta wave. Phase-lockings and chaotic responses occurred depending on stimulus parameters under the above conditions. Trajectories of the chaotic responses in the two-dimensional phase space (V, dV/dt) reconstruct strange attractors, and stroboscopic cross-sections of each attractor show stretching and folding process. Each one-dimensional strobomap of the chaotic responses is a noninvertible function with an unstable fixed point. This is undoubted evidence for chaotic responses of the somatosensory cortex in vivo. Power spectra well characterize the periodic and the chaotic responses. Positive Lyapunov exponents and low, noninteger correlation dimensions of the chaotic responses are consistent with the above evidence. Consequently, four kinds of chaotic responses were classified. A periodic-chaotic transition sequence was observed at a relatively low stimulus current when the frequency of the stimulation was varied. A cascade of period-doubling bifurcations was also observed on a route from the region of the 1:1 phase-locking to one of the regions of the chaotic responses.     

一类具有不确定性时滞大系统的鲁棒稳定条件

根据微分方程理论和矩阵指数特性，讨论了一类具有时变时滞线性大系统的稳定性，并导出了具有时滞相关和时滞无关线性系统稳定性的充分条件，然后讨论了此类大系统的鲁棒稳定条件，并与相关文献进行了比较，计算实例表明，所得出的结果改进了现有的研究成果。     

Constructive model predictive control for constrained nonlinear systems

This paper develops a new model predictive control (MPC) design for stabilization of continuous‐time nonlinear systems subject to state and input constraints. The key idea is to construct an analytic form of the controller with some undetermined parameters and to calculate the parameters by minimizing online a performance index. By using the method of control Lyapunov functions (CLFs), we construct an appropriate variation on Sontag's formula, with one degree of freedom reflecting ‘decay rate’ of CLFs. Moreover, the constructed univariate control law is used to characterize the terminal region that guarantees the feasibility of the optimal control problem. Provided that the initial feasibility of the optimization problem is satisfied, the stability of the control scheme can be guaranteed. An example is given to illustrate the application of the constructive MPC design. Copyright © 2008 John Wiley & Sons, Ltd.