随机变时滞神经网络的全局渐近稳定性

研究了一类具有变时滞随机神经网络模型平衡点的全局渐近稳定性问题,通过构造李亚普诺夫函数并利用线性矩阵不等式理论,得出了随机变时滞神经网络的全局渐近稳定性的充分条件。     

变时滞随机递归神经网络的全局指数稳定性

利用自由权值矩阵和不等式分析技巧,研究了一类随机变时滞神经网络的全局指数稳定性问题.该模型中考虑了神经网络的外部随机扰动因素,更加接近真实网络.通过构造适当的Lyapunov-Krasovskii泛函,以线性矩阵不等式形式给出了的全局指数稳定性判据,能够利用Matlab的LMI工具箱很容易地进行检验.此外,仿真结果进一步证明了结论的有效性.     

不确定随机变时滞神经网络的全局渐进稳定性

采用It(o)'s微分公式和不等式分析技巧,研究了一类不确定随机变时滞神经网络的全局渐进稳定性问题.该模型同时考虑了神经网络模型的两种扰动因素,即随机扰动与不确定性扰动.不确定性参数是时变且范数有界的.通过构造适当的Lyapunov泛函,以线性矩阵不等式形式给出了平衡点在均方根意义下的全局渐进稳定性判据,能够利用LMI工具箱很容易地进行检验.此外,仿真示例证明了结论的有效性.     

具有混合时滞的随机神经网络的无源性分析

针对一类具有混合时滞的随机神经网络,研究其无源性分析问题.假设神经网络的离散状态时滞是不确定的,看成一个标称值受时变扰动;神经网络的分布式状态时滞是定常的.通过构造适当的离散化Lyapunov-Krasovskii泛函,并结合自由权矩阵方法,以线性矩阵不等式的形式给出了保证具有混合时滞的随机神经网络无源的时滞依赖充分条件.     

具有时滞的高阶Hopfield型神经网络的稳定性

通过Lyapunov泛函的方法，对具有时滞的高阶连续型Hopfield神经网络平衡点的稳定性进行分析，利用Razumikhin定理得到平衡点全局一致渐近稳定的时滞相关与时滞无关充分条件。     

Mean Square Exponential Stability for Uncertain Delayed Stochastic Neural Networks with Markovian Jump Parameters

This paper is concerned with the problem of delay-dependent mean square exponential stability for a class of delayed stochastic Hopfield neural networks with Markovian jump parameters. The delays here are time-varying delays. Based on a new Lyapunov–Krasovskii functional, delay-dependent stability conditions are derived by means of linear matrix inequalities (LMIs). It is shown that the proposed results can contain some existing stability conditions as a special case. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method, and the simulations show that our results are less conservative than the existing ones.     

基于神经网络的联合混沌时间序列的预测研究

提出了利用前馈神经网络预测联合混沌序列,通过引用著名的Henon和Lozi混沌系统作为仿真实验产生联合混沌信号序列。预测结果证明,用改进的BP算法训练的NN可以完全预测联合混沌信号序列。     

Delay-Dependent Exponential Stability for Uncertain Stochastic Hopfield Neural Networks With Time-Varying Delays

This paper provides new delay-dependent conditions that guarantee the robust exponential stability of stochastic Hopfield type neural networks with time-varying delays and parameter uncertainties. Both the cases of the time-varying delays which are differentiable and may not be differentiable are considered. The stability conditions are derived by using the recently developed free-weighting matrices technique and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria. It is shown that the proposed stability results are less conservative than some previous ones in the literature.      

Mode-Dependent H_{\infty } Filtering for Stochastic Markovian Switching Genetic Regulatory Networks with Leakage and Time-Varying Delays

In this paper, the \(H_{\infty }\) filtering problem is considered for Markovian switching genetic regulatory networks (GRNs) with mode-dependent leakage and time-varying delays along intrinsic molecular fluctuations and extrinsic molecular noises. The aim of this paper is to design a filter to estimate the true concentrations of mRNAs and proteins. By choosing suitable Lyapunov–Krasovskii functionals and reciprocally convex combination approach, sufficient conditions are obtained to ensure that the filtering error system is globally stochastically stable in the mean-square sense with the prescribed \(H_{\infty }\) disturbance attenuation levels. The existence of the designed \(H_{\infty }\) filters is expressed in terms of linear matrix inequalities (LMIs), which can be easily solved by using Matlab LMI toolbox. Also the corresponding results are obtained for the GRNs without leakage delays. Finally, two numerical examples are given, which include a repressilator model of Escherichia coli to illustrate the effectiveness of the proposed theoretical results.     

基于LMI方法的时滞BAM神经网络的全局稳定性分析

对于时滞双向联想记忆(DBAM)神经网络的平衡点的稳定性问题,目前人们已经得到了很多富有意义的成果。该文提出一种新的神经网络模型标准神经网络模型(SNNM),通过状态的线性变换,将DBAM神经网络转化为时滞SNNM(DSNNM),并利用有关DSNNM的稳定性的一些结论,得到DBAM神经网络平衡点的全局渐近稳定性的充分条件。这些条件都以线性矩阵不等式(LMI)的形式给出,容易验证,保守性低。该方法扩展了以前的稳定性结果,同时也适用于其它类型的递归神经网络(时滞或非时滞)的稳定性分析。     

Global Stability of Fuzzy Cellular Neural Networks with Mixed Delays and Leakage Delay Under Impulsive Perturbations

This paper investigates the global asymptotic stability of a kind of fuzzy cellular neural networks with mixed delays under impulsive perturbations. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delays, and continuously distributed delays. By using the quadratic convex combination method, reciprocal convex approach, Jensen integral inequality, and linear convex combination technique, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.     

多比例时滞细胞神经网络的同步性

基于混沌同步控制在保密通信及优化等诸多范畴的遍及应用,本文研究一类驱动-响应系统的同步性问题,包含指数同步性和多项式同步性.这里以一类带多比例时滞的细胞神经网络作为驱动系统,一类不带比例时滞的细胞神经网络作为响应系统.在激活函数满足Lipschitz的条件下,通过设计合适的时滞依赖的控制器,且利用Lyapunov稳定性理论及一些不等式分析探讨误差系统的稳定性,进而得到所研究的驱动-响应系统同步性的两个判定标准,然后给出数值模拟验证所得结果.     

Input-to-State Stability of Memristive Neural System with Time Delays

Memristive neural systems are a ground breaking concept that is helping us understand the behavior of electronic brain. In this paper, a general class of memristive neural systems with time delays is formulated and investigated. Several succinct criteria are given to ascertain the input-to-state stability via nonsmooth analysis and control theory. These conditions, which can be directly derived from the parameters of the system, are easily verified. The obtained results extend some previous works on conventional neural systems. A numerical example is provided to show the efficiency of the proposed approach.     

Delay-Probability-Distribution-Dependent Stability of Uncertain Stochastic Genetic Regulatory Networks with Time-Varying Delays

This paper investigates the delay-probability-distribution-dependent stability problem of uncertain stochastic genetic regulatory networks (SGRNs) with time-varying delays. The information of the probability distribution of the time-delay is considered and transformed into parameter matrices of the transferred SGRNs model. Based on the Lyapunov–Krasovskii functional and a stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is obtained in the linear matrix inequality (LMI) form such that delayed SGRNs are robustly globally asymptotically stable in the mean square for all admissible uncertainties. Three numerical examples are given to illustrate the effectiveness of our theoretical results.     

混沌光学系统的神经网络自适应控制研究

提出一种用于混沌光学系统控制的神经网络自适应控制技术。以一前向神经网络作为受控混沌光学系统的系统辩识器，由此神经网络系统辩识器与受控混沌光学系统输出差值作为负反馈对受控混沌光学系统控制参数进行调整达到控制目的。由于所使用神经网络系统辩识器在常规ＢＰ算法的支持下可从受控混沌光学系统的输出时间序列进行动力学模型重构，因而特别适用于对未知动力学表述的混沌光学系统进行控制。以对布喇格声光双稳混沌系统的系统辩识及自适应控制为例，对此神经网络自适应控制技术可行性进行了示例证明。     

Pinning Synchronization of Independent Chaotic Systems on Complex Networks with Double Delays

Wireless Personal Communications - In this paper, aiming at the problem of different signals acting on the same node on a complex network with double time delay, two independent chaotic systems are...     

具有变时滞的静态神经网络新的稳定性条件

考虑一类具有变时滞的静态神经网络的渐近稳定性问题,基于Lyapunov稳定性理论,时滞分解的思想,并利用时滞导数的上下界,得到了线性矩阵不等式表示的新的渐近稳定性条件,最后,两个数值例子表明所得结果较一些现存结果具有更小的保守性。     

具反映扩散无穷连续分布时滞神经网络的全局渐近稳定性

利用同伦不变性原理、Dini导数、格林公式,研究了一类具反应扩散的无穷时滞神经网络系统的平衡点的存在唯一性和全局渐近稳定性.在去掉对神经元的激励函数有界性、可微性、去掉对平均时滞∫∞0sk(s)ds有界性的要求,仅要求激励函数满足Lipchitz条件等较宽松的条件下,获得了该类系统的全局渐近稳定性的充分条件.改进和推广了已有文献的最新结果.并用实例说明了这些获得的结果的有效性.