多比例时滞细胞神经网络的指数周期性与稳定性

研究了一类具多比例时滞细胞神经网络的全局指数周期性与稳定性.通过变换y(t)=x(e~t)将具多比例时滞的细胞神经网络变换成具常时滞变系数的细胞神经网络,利用一些分析技巧与构造合适的Lyapunov泛函,得到系统的周期解存在唯一且全局指数周期的时滞依赖的充分条件,判断方法简单易验证.并给出了两个例子及其数值仿真结果以支持所得结论.     

Robust exponential stabilization of a class of delayed neural networks with reaction-diffusion terms

In this paper, the problem of global robust exponential stabilization for a class of neural networks with reaction-diffusion terms and time-varying delays which covers the Hopfield neural networks and cellular neural networks is investigated. A feedback control gain matrix is derived to achieve the global robust exponential stabilization of the neural networks by using the Lyapunov stability theory, and the stabilization condition can be verified if a certain Hamiltonian matrix with no eigenvalues on the imaginary axis. This condition can avoid solving an algebraic Riccati equation. Finally, a numerical simulation illustrates the effectiveness of the results.     

变时延神经网络的全局指数稳定性及收敛性

利用Lyapunov泛函方法和线性矩阵不等式（LMI）技术,通过引入一系列参数,给出全局指数稳定的平衡点的判别条件和时延的最大上界和神经网络的收敛速度,所得结果较之一些文献中的结果简单、实用并且对于具体设计带时延神经网络有重要的指导意义.最后,通过实例表明给出的判定条件是有效、可行的.     

A novel global exponential stability result for discrete-time cellular neural networks with variable delays

Global exponential stability is considered for a class of discrete-time cellular neural networks with variable delays. By employing a discrete Halanay inequality, a new result is presented ensuring global exponential stability of the unique equilibrium point of the networks. The result extends and improves the earlier publications due to the fact that it removes some restrictions on the delay. An example is given to illustrate the effectiveness of the global exponential stability condition provided here.     

Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays

This paper concerns the problem of global exponential synchronization for a class of memristor-based Cohen–Grossberg neural networks with time-varying discrete delays and unbounded distributed delays. The drive-response set is discussed. A novel controller is designed such that the response (slave) system can be controlled to synchronize with the drive (master) system. Through a nonlinear transformation, we get an alternative system from the considered memristor-based Cohen–Grossberg neural networks. By investigating the global exponential synchronization of the alternative system, we obtain the corresponding synchronization criteria of the considered memristor-based Cohen–Grossberg neural networks. Moreover, the conditions established in this paper are easy to be verified and improve the conditions derived in most of existing papers concerning stability and synchronization for memristor-based neural networks. Numerical simulations are given to show the effectiveness of the theoretical results.     

一类具变时滞的模糊BAM神经网络的平衡点的指数稳定性(英文)

研究一类具变时滞的模糊BAM神经网络.利用拓扑度论和微分不等式,获得了该类网络平衡点的存在性、唯一性和全局指数稳定性的充分条件.一个例子用来解释本文获得的结果.     

Relaxed stability conditions for delayed recurrent neural networks with polytopic uncertainties

This paper investigates the problem of stability analysis for recurrent neural networks with time-varying delays and polytopic uncertainties. Parameter-dependent Lypaunov functionals are employed to obtain sufficient conditions that guarantee the robust global exponential stability of the equilibrium point of the considered neural network. The derived stability criteria are expressed in terms of a set of relaxed linear matrix inequalities, which can be easily tested by using commercially available software. Two numerical examples are provided to demonstrate the effectiveness of the proposed results.     

Mean square exponential and robust stability of stochastic discrete-time genetic regulatory networks with uncertainties

This paper aims to analyze global robust exponential stability in the mean square sense of stochastic discrete-time genetic regulatory networks with stochastic delays and parameter uncertainties. Comparing to the previous research works, time-varying delays are assumed to be stochastic whose variation ranges and probability distributions of the time-varying delays are explored. Based on the stochastic analysis approach and some analysis techniques, several sufficient criteria for the global robust exponential stability in the mean square sense of the networks are derived. Moreover, two numerical examples are presented to show the effectiveness of the obtained results.     

New criteria of almost periodic solution for bam neural networks with delays and impulsive effects

This paper presents some sufficient conditions for the existence and global exponential stability of the almost periodic solution for impulsive bi-directional associative memory neural networks with time-varying delays by using Lyapunov functional and Gronwall-Bellmans inequality technique. Comparing with known literatures, the results of this paper are new and they complement previously known results.     

具常数时滞细胞神经网络概周期解

利用矩阵不等式的分析技巧和Banach空间中不动点定理,得到了具常数时滞细胞神经网络概周期解的存在性、唯一性和全局指数稳定性,推广和改进了已有文献的结论。     

带脉冲的BAM神经网络的全局指数稳定性

利用M矩阵理论,推广的微分不等式和Lyapunov函数,研究了一类带时滞和脉冲的BAM神经网络平衡点的存在唯一性和全局指数稳定性条件.文中推广了以往文献脉冲函数的形式,无需时滞的可导性要求,从而减弱了以往结论的条件,并且可以估计网络的指数收敛速率.     

Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays

In this article, we consider a class of neutral impulsive shunting inhibitory cellular neural networks with time varying coefficients and leakage delays. We study the existence and the exponential stability of the piecewise differentiable pseudo almost-periodic solutions and establish sufficient conditions for the existence and exponential stability of such solutions. An example is provided to illustrate the theory developed in this work.     

具有分布时滞离散Cohen-Grossberg神经网络的周期解

讨论了一类具有分布时滞离散Cohen-Grossberg神经网络模型,利用M-矩阵理论与适合的Lypunov函数,得到该类模型周期解的存在性与全局指数稳定性．     

具有时滞的广义BAM脉冲神经网络的全局指数稳定性

本文讨论一类具有时滞的广义双向联想记忆（BAM）脉冲神经网络的指数稳定性．利用Banach空间的不动点定理和Lyapunoy泛函,在不假定激励函数有界、单调和可徽的条件下,得到了平衡点的存在唯一性定理及其为全局指数稳定的充分条件．文末通过实例阐释了所获结论的有效性．     

变时滞区间细胞神经网络的全局鲁棒稳定性

利用拓扑度理论和Liapunov泛函方法讨论了变时滞区间细胞神经网络的全局鲁棒稳定性．给出了实用有效的判定条件,推广了有关文献中的结果．     

Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control

This paper investigates drive-response synchronization for a class of neural networks with time-varying discrete and distributed delays (mixed delays) as well as discontinuous activations. Strict mathematical proof shows the global existence of Filippov solutions to neural networks with discontinuous activation functions and the mixed delays. State feedback controller and impulsive controller are designed respectively to guarantee global exponential synchronization of the neural networks. By using Lyapunov function and new analysis techniques, several new synchronization criteria are obtained. Moreover, lower bound on the convergence rate is explicitly estimated when state feedback controller is utilized. Results of this paper are new and some existing ones are extended and improved. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.     

高阶S-分布时滞广义细胞神经网络的全局指数稳定性

研究一类高阶S-分布时滞广义细胞神经网络的稳定性.利用一些分析技巧,通过构造恰当的Lebesgue-Stieltjes积分型Lyapunov泛函,得到系统全局指数稳定的充分条件,判断方法简单易验证.最后给出了主要定理的一个实例,表明结论的有效性.     

Global convergence of delayed neural network systems

In this paper, without assuming the boundedness, strict monotonicity and differentiability of the activation functions, we utilize a new Lyapunov function to analyze the global convergence of a class of neural networks models with time delays. A new sufficient condition guaranteeing the existence, uniqueness and global exponential stability of the equilibrium point is derived. This stability criterion imposes constraints on the feedback matrices independently of the delay parameters. The result is compared with some previous works. Furthermore, the condition may be less restrictive in the case that the activation functions are hyperbolic tangent.     

New criteria on global exponential stability of bam neural networks with distributed delays and reaction-diffusion terms

This paper presents new theoretical results on global exponential stability of bi-directional associative memory neural networks with distributed delays and reaction-diffusion terms based on the inequality technique, Lyapunov functional, and analysis technique. The results remove the usual assumption that the activation functions are of monotonous or differential character. Exponential converging velocity index is estimated, which depends on the delay kernel functions and system parameters. Finally, two numerical examples are given to show the validity and feasibility of our results.     

Global and robust stability of interval Hopfield neural networks with time-varying delays

In this paper, we investigate the problem of global and robust stability of a class of interval Hopfield neural networks that have time-varying delays. Some criteria for the global and robust stability of such networks are derived, by means of constructing suitable Lyapunov functionals for the networks. As a by-product, for the conventional Hopfield neural networks with time-varying delays, we also obtain some new criteria for their global and asymptotic stability.