二次规划问题的新型时滞投影神经网络的稳定性分析

本文针对求解有等式约束的二次规划问题的时滞投影神经网络,提出一种所有神经元皆存在时滞情况的新型网络模型。利用Gronwall不等式和Halanay不等式,严格证明了所提网络模型的全局指数稳定性。研究结果表明,所提网络模型的解能够渐进收敛于原问题的最优解,具有计算迅速和精度较高等特点。数值仿真结果验证了所提网络模型的可行性与有效性。     

离散Hopfield双向联想记忆神经网络的稳定性分析

首先将离散Hopfield双向联想记忆神经网络转化成一个特殊的离散Hopfield网络 模型.在此基础上,对离散Hopfield双向联想记忆神经网络的全局渐近稳定性和全局指数稳 定性进行了新的分析.证明了神经网络连接权矩阵在给定的约束条件下有唯一的而且是渐近 稳定的平衡点.利用Lyapunov方程正对角解的存在性得到了几个判定平衡点为全局渐近稳 定和全局指数稳定的充分条件.这些条件可以用于设计全局渐近稳定和全局指数稳定的神经 网络.所做的分析扩展了以前的稳定性结果.     

线性混合耦合切换网络的全局指数同步研究

研究具有子系统时变时延和节点间耦合时延的线性混合耦合切换网络的全局指数同步问题。应用切换系统的稳定性理论对具有特殊切换信号和切换拓扑结构的复杂动态网络的同步性问题进行研究,并以线性矩阵不等式形式给出一个时延相关的充分条件,该条件保证了该类网络在应用平均驻留时间方法时能够达到全局指数同步。最后给出一个实例验证了结论的正确性。     

一类随机人口发展系统的指数稳定性

对人口系统的讨论 ,通常的数学模型没有考虑外界环境对系统的影响 .在假设随机的外界环境对迁移产生扰动的条件下 ,给出Hilbert空间中一类随机时变人口发展系统 .对随机时变人口发展系统的均方稳定性和指数稳定性进行了讨论 .利用Burkholder_Davis_Gundy不等式 ,Gronwall引理和Kolmogorov不等式得到了均方稳定和指数稳定的充分条件 .最后提出如果生育率选作控制变量 ,系统仍然是均方和指数稳定的 ,并可进一步讨论它的最优控制问题     

一类变时滞神经网络的全局指数稳定性

在不要求激活函数有界的前提下,利用Lyapunov泛函方法和线性矩阵不等式(LMI)分析技巧,研究了一类变时滞神经网络平衡点的存在性和全局指数稳定性.给出判别网络全局指数稳定性的判据,推广了现有文献中的一些结果.这些判据具有LMI的形式,进而易于验证.仿真例子表明了所得结果的有效性.     

具漏泄时滞的细胞神经网络多周期性分析

针对一类具有漏泄时滞细胞神经网络模型,首先给出该类网络的周期环在饱和区局部指数收敛的充分条件.研究表明,一个n维网络可以有2n个周期环存在于饱和区,并且这些周期环是局部指数收敛的.然后,研究了该时滞细胞神经网络指数周期的一个特殊情形--指数稳定.数值例子和仿真结果验证了所得结果的有效性.     

一类时滞神经网络系统的指数稳定性

利用矩阵测度研究了一类时滞神经网络系统的指数稳定性,给出保证神经网络系统指数稳定的充分条件.输出函数不需要满足Lipschitz条件,且也不要求它们可微或严格单调递增.在关联矩阵不对称的情况下,所得到的结论仍然成立.最后一个数值例子验证了判据的有效性.     

时变时滞离散递归神经网络系统的状态估计器设计

研究时滞离散递归神经系统的状态估计问题.通过网络输出对神经元的状态进行估计.在较弱的激活函数假设下,通过构造一个新的Lyapunov泛函,引入一个自由权矩阵,并结合Jensen不等式得到了确保误差系统全局指数稳定的充分条件.所得条件依赖于时变时滞的上界和下界,并以线性矩阵不等式的形式给出.最后的数值算例表明了所提出方法的有效性.     

一类推广的二元神经网络的稳定性分析

利用不动点定理和微分不等式的分析技巧,引入多个变时滞,去掉对激活函数光滑性与有界性的假设,研究了一类推广的二元神经网络的平衡点的存在性,得到了系统存在平衡点和全局指数稳定性的新的充分条件．     

具时滞脉冲细胞神经网络的全局指数稳定性

研究了一类新的具有脉冲的时滞细胞神经网络系统模型,引入了一类新的脉冲条件,在不假设激励函数的有界性、单调性和光滑性的条件下,得到了系统平衡点的存在性、唯一性及全局指数稳定性的一些新的充分条件,并得到了指数收敛速率.     

A new result on global exponential robust stability of neural networks with time-varying delays

In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.     

Novel criteria for global robust exponential stability of neural networks with time-varying delays via LMI approach

The article addresses the problem of global robust exponential stability of interval neural networks with time-varying delays. On the basis of linear matrix inequality technique and M-matrix theory, some novel sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed interval neural networks are presented. It is shown that our results improve and generalize some previously published ones. Some numerical examples and simulations are given to show the effectiveness of the obtained results.     

Global exponential stability in Lagrange sense for quaternion-valued neural networks with leakage delay and mixed time-varying delays

This paper deals with the global exponential stability in Lagrange sense for quaternion-valued neural networks (QVNNs) with leakage delay, discrete time-varying delays and distributed delays. By structuring an advisable Lyapunov–Krasovskii functional in quaternion field, and adopting free-weighting-matrix method and inequality technique, a sufficient condition in quaternion-valued linear matrix inequality (LMI) to guarantee the global exponential stability in Lagrange sense is acquired, and the domain of attraction is estimated. A numerical example with simulations is supplied to confirm the availability and feasibility of the raised result.     

On global exponential stability for impulsive cellular neural networks with time-varying delays

In this paper, the problem of global exponential stability for cellular neural networks (CNNs) with time-varying delays and fixed moments of impulsive effect is studied. A new sufficient condition has been presented ensuring the global exponential stability of the equilibrium points by using piecewise continuous Lyapunov functions and the Razumikhin technique combined with Young’s inequality. The results established here extend those given previously in the literature. Compared with the method of Lyapunov functionals as in most previous studies, our method is simpler and more effective for stability analysis.     

Global Asymptotic Robust Stability and Global Exponential Robust Stability of Neural Networks with Time-Varying Delays

In this paper, based on nonnegative matrix theory, the Halanay’s inequality and Lyapunov functional, some novel sufficient conditions for global asymptotic robust stability and global exponential robust stability of neural networks with time-varying delays are presented. It is shown that our results improve and generalize several previous results derived in the literatures. From the obtained results, some linear matrix inequality criteria are derived. Finally, a simulation is given to show the effectiveness of the results.     

Periodic Dynamics for Memristor-based Bidirectional Associative Memory Neural Networks with Leakage Delays and Time-varying Delays

This paper deals with a class of memristor-based bidirectional associative memory (BAM) neural networks with leakage delays and time-varying delays. With the aid of the framework of Filippov solutions, Chain rule and some inequality techniques, a sufficient condition which ensures the boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks with leakage delays and time-varying delays is established. Applying a new approach involving Yoshizawa-like theorem, we prove the existence of periodic solution of the memristor-based BAM neural networks. By using the theory of set-valued maps and functional differential inclusions, Lyapunov functional, a set of sufficient conditions which guarantee the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks are derived. An example is given to illustrate the applicability and effectiveness of the theoretical predictions. The results obtained in this paper are completely new and complement the previously known studies of Li et al. [Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays, Neural networks 75 (2016) 97-109.]     

Global exponential stability for neutral-type BAM neural networks with time-varying delays

In this article, the global exponential stability of neutral-type bidirectional associative memory (BAM) neural networks with time-varying delays is analysed by utilizing the Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach. New sufficient conditions ensuring the global exponential stability of neutral-type BAM neural networks is obtained by using the powerful MATLAB LMI control toolbox. In addition, an example is provided to illustrate the applicability of the result.     

Global exponential stability of a class of Hopfield neural networks with delays

This paper investigates global exponential stability of a class of Hopfield neural networks with delays based on contraction mapping principle, Lyapunov function and inequality technique. Some sufficient conditions are derived that ensure the existence, uniqueness, global exponential stability of equilibrium point of the neural networks. Finally, an illustrative numerical example is given to demonstrate the effectiveness of our results.     

变时滞神经网络的全局指数稳定性

利用M矩阵理论,同构理论以及不等式技巧,研究了一类变时滞神经网络平衡点的存在性和惟一性问题。同时利用M矩阵理论,反证法以及不等式技巧,得到了变时滞神经网络系统惟一的平衡点的全局指数稳定性的充分条件。通过判断由神经网络的权系数、自反馈函数以及激励函数构造的矩阵是否为M矩阵,即可以检验该变时滞神经网络系统的全局指数稳定性。该判据易于用Matlab进行检验,最后给出一个仿真示例进一步证明了判据的有效性。