Global Exponential Stability for Impulsive BAM Neural Networks with Distributed Delays on Time Scales

In this paper, by utilizing the time scale calculus theory, topological degree theory and Hölder’s inequality on time scales, we analyze a class of impulsive BAM neural networks with distributed delays on time scales. Some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the equilibrium point. Finally, an example is provided to demonstrate the effectiveness of the results.     

具有时变时滞的递归神经网络的渐近稳定性分析

当神经网络应用于最优化计算时,理想的情形是只有一个全局渐近稳定的平衡点,并且以指数速度趋近于平衡点,从而减少神经网络所需计算时间.研究了带时变时滞的递归神经网络的全局渐近稳定性.首先将要研究的模型转化为描述系统模型,然后利用Lyapunov-Krasovskii稳定性定理、线性矩阵不等式(LMI)技术、S过程和代数不等式方法,得到了确保时变时滞递归神经网络渐近稳定性的新的充分条件,并将它应用于常时滞神经网络和时滞细胞神经网络模型,分别得到了相应的全局渐近稳定性条件.理论分析和数值模拟显示,所得结果为时滞递归神经网络提供了新的稳定性判定准则.     

Global Exponential Stability and Existence of Periodic Solution of Impulsive Cohen–Grossberg Neural Networks with Distributed Delays on Time Scales

On time scales, by using the continuation theorem of coincidence degree theory, M-matrix theory and constructing some suitable Lyapunov functions, some sufficient conditions are obtained for the existence and exponential stability of periodic solutions of impulsive Cohen–Grossberg neural networks with distributed delays, which are new and complement of previously known results. Finally, an example is given to illustrate the effectiveness of our main results.     

Exponential Stability of Positive Recurrent Neural Networks with Multi-proportional Delays

Neural Processing Letters - This paper presents some new results on the existence, uniqueness and generalized exponential stability of a positive equilibrium for positive recurrent neural networks...     

带两个不同时延神经网络的稳定性研究

讨论了带两个不同时延且有两个神经元系统的局部稳定性,得到了判定神经网络稳定性的一些准则,这些准则有的是与时延有关,而有的是与时延无关（这种情形也称为“无害时延”）;研究方法对于带不同时延且多个神经元网络的稳定性的研究有重要的指导意义。     

Delay-Dependent Stability for Recurrent Neural Networks With Time-Varying Delays

This brief is concerned with the stability for static neural networks with time-varying delays. Delay-independent conditions are proposed to ensure the asymptotic stability of the neural network. The delay-independent conditions are less conservative than existing ones. To further reduce the conservatism, delay-dependent conditions are also derived, which can be applied to fast time-varying delays. Expressed in linear matrix inequalities, both delay-independent and delay-dependent stability conditions can be checked using the recently developed algorithms. Examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed result.      

Existence and Global Exponential Stability of Almost Periodic Solution for High-Order BAM Neural Networks with Delays on Time Scales

In this paper, by using a fixed point theorem and by constructing a suitable Lyapunov functional, we study the existence and global exponential stability of almost periodic solution for high-order bidirectional associative memory neural networks with delays on time scales. An examples shows the feasibility of our main results.     

含离散和分布时变时延神经网络系统的指数稳定性

针对一类含有离散和分布时延神经网络,在神经激活函数较弱的约束条件下,通过定义一个更具一般性的Lyapunov泛函,使用凸组合技术,得到了新的基于线性矩阵不等式表示的指数稳定性判据.与现有结果相比,这些判据具有较小的保守性.仿真算例表明,得到的结果是有效的且保守性小.     

一类时滞神经网络的全局指数稳定性

利用M-矩阵和拓扑学等有关知识,通过构建向量李雅普诺夫函数,研究了一类包含分布时滞和可变时滞的神经网络的平衡点的存在性、唯一性及其全局指数稳定性。在没有假定激励函数有界、可微的情况下,得到了该类神经网络平衡点的存在性、唯一性及其在平衡点全局指数稳定的充分判据。该判据计算简便,且与时间滞后量无关,便于在实践中应用。文中给出了一个算例。     

Stability Analysis of Stochastic Fuzzy Cellular Neural Networks With Time-Varying Delays and Reaction-Diffusion Terms

In this paper, a class of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms is investigated. By using Lyapunov–Krasovskii functional and stochastic analysis approaches, new and less conservative delay-derivative-dependent stability criteria are presented to guarantee the neural networks to be globally exponentially stable in the mean square for all admissible stochastic perturbations. Numerical simulations are carried out to illustrate the main results.     

Global Asymptotic Stability of Fuzzy Cellular Neural Networks with Unbounded Distributed Delays

Asymptotic stability problem of a class of fuzzy cellular neural networks with unbounded distributed delays is studied. New stability criteria are derived by employing a Lyapunov-Krasovskii functional and using LMI approach. Numerical examples are provided to illustrate the effectiveness and less conservativeness of the developed techniques.     

Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays

This brief addresses the stability analysis problem for stochastic neural networks (SNNs) with discrete interval and distributed time-varying delays. The interval time-varying delay is assumed to satisfy $0≪d_{1}leq d(t) leq d_{2}$ and is described as $d(t)= d_{1}+h(t)$ with $0leq h(t) leq d_{2}-d_{1}$. Based on the idea of partitioning the lower bound $d_{1}$, new delay-dependent stability criteria are presented by constructing a novel Lyapunov–Krasovskii functional, which can guarantee the new stability conditions to be less conservative than those in the literature. The obtained results are formulated in the form of linear matrix inequalities (LMIs). Numerical examples are provided to illustrate the effectiveness and less conservatism of the developed results.      

Pseudo Almost Periodic Solution of Recurrent Neural Networks with D Operator on Time Scales

This paper is concerned with a class of neutral type recurrent neural networks with time-varying delays, distributed delay and D operator on time–space scales which unify the continuous-time and the discrete-time recurrent neural networks under the same framework. Some sufficient conditions are given for the existence and the global exponential stability of the pseudo almost periodic solution by using inequality analysis techniques on time scales, fixed point theorem and the theory of calculus on time scales. An example is given to show the effectiveness of the derived results via computer simulations.

     

Hopf Bifurcation Analysis of a Reaction-Diffusion Neural Network with Time Delay in Leakage Terms and Distributed Delays

In this paper, a reaction-diffusion neural network with time delay in leakage terms and distributed synaptic transmission delays under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equation, the local stability of the trivial uniform steady state and the existence of Hopf bifurcation are established. By using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulae are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.     

Improved Delay-Derivative-Dependent Stability Analysis for Generalized Recurrent Neural Networks with Interval Time-Varying Delays

Neural Processing Letters - In this paper, the problem of delay-derivative-dependent stability analysis for generalized neural networks with interval time-varying delays is considered. First, we...     

Synchronization of Drive-Response Networks With Delays on Time Scales

<正>Dear Editor,This letter deals with the synchronization in drive-response networks with discrete and distributed delays on time scales. Based on the theory of calculus on time scales, Lyapunov functional method and inequality technique, we obtain new sufficient conditions to ensure synchronization criteria which are dependent on boundedness of grainness but independent of the types of delays. Numerical simulations are given to illustrate the effectiveness of our new results.     

On p-th Moment Exponential Stability for Stochastic Cellular Neural Networks with Distributed Delays

International Journal of Control, Automation and Systems - In this paper, a class of stochastic cellular neural networks with distributed delays are investigated. With the help of the method of...     

Further Improvement on Delay-range-dependent Stability Criteria for Delayed Recurrent Neural Networks with Interval Time-varying Delays

International Journal of Control, Automation and Systems - This paper considers the problem of delay-range-dependent stability analysis for a class of delayed recurrent neural networks (DRNNs) with...     

Finite Time Stability Analysis of Fractional-Order Complex-Valued Memristive Neural Networks with Proportional Delays

Neural Processing Letters - In this paper, finite time stability analysis of fractional-order complex-valued memristive neural networks with proportional delays is investigated. Under the framework...