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。     

一类时滞神经网络的指数稳定性分析

本文研究了一类具有分布时滞和参数不确定性的神经网络指数稳定性问题。通过构造适当的Lyapunov-Krasovskii泛函,引入自由权矩阵,以及利用一些不等式技巧,得出了一个新颖的时滞依赖指数稳定性判据。判据条件是以线性矩阵不等式(LMI)的形式给出,便于直接应用Matlab中LMI工具箱进行验证。最后给出的数值例子说明了本文结论的有效性和优越性。     

一类时滞神经网络的指数稳定性分析北大核心CSCD

本文研究了一类具有分布时滞和参数不确定性的神经网络指数稳定性问题。通过构造适当的Lyapunov-Krasovskii泛函,引入自由权矩阵,以及利用一些不等式技巧,得出了一个新颖的时滞依赖指数稳定性判据。判据条件是以线性矩阵不等式(LMI)的形式给出,便于直接应用Matlab中LMI工具箱进行验证。最后给出的数值例子说明了本文结论的有效性和优越性。     

具有修正的Lelie-Gower项Holling-III类时滞捕食系统的Hopf分支

研究了一类具有修正的Leslie-Gower项与Holling-III类功能性反应函数的时滞捕食系统. 以时滞为分支参数, 讨论系统正平衡点的局部稳定性, 给出系统产生Hopf分支的时滞关键值. 进一步, 确定系统Hopf分支的方向与分支周期解稳定性, 并对系统全局分支周期解的存在性进行讨论. 最后, 利用仿真实例验证理论分析结果的正确性.     

BAM神经网络周期解的存在性与稳定性

利用不动点理论、Lyapunov泛函,研究了具变时滞的BAM神经网络周期解的存在性、唯一性和全局指数稳定性问题。所得的充分判别标准由线性矩阵不等式所表示,可以较容易地由Matlab进行验证。仿真实例表明,得到的判据是有效的。     

时滞切换不确定神经网络系统的指数稳定性

本文研究了具有无穷时滞切换不确定细胞神经网络(UCNNs)系统任意切换下的指数稳定性.利用同胚映射和M-矩阵理论,得到UCNNs系统平衡点存在性,唯一性和指数稳定性的充分条件;利用Lyapunov泛函方法,研究了时滞切换UCNNs系统任意切换下的鲁棒指数稳定性,并得到确保系统全局指数稳定的充分条件.     

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.     

时滞反应扩散Hopfield神经网络的滑动模控制

研究了一类具有S--分布时滞和反应扩散项的Hopfield神经网络的滑动模控制问题. 首先改进了一类Hanalay不等式, 给出了一种范数不等式. 然后通过等效控制方法建立了系统的滑动模态方程, 并利用不等式技巧分析了它的吸引集的存在性和零点的指数稳定性. 在此基础上设计了变结构控制器, 给出了运动轨线到达滑动模态区的时间估计. 最后给出了一个例子验证了本文的结果, 并利用MATLAB作出了仿真.     

脉冲时滞Hopfield神经网络的全局指数稳定性

研究一类具有脉冲控制的时滞Hopfideld神经网络的全局指数稳定性,通过Lyapunov-Krasovskii稳定性理论和Halanay不等式等方法,构造合适的Lyapunov泛函,利用不等式技巧得到了确保时滞神经网络在脉冲控制下全局指数稳定的一个充分条件,保证了Hofidd神经网络在脉冲控制下的全局指数稳定,并估计了系统的指数收敛率.为了便于计算和验证结论的有效性,给出一个简化的充分条件.最后通过数值实例的实验仿真证实了结论的有效性、可行性.     

时滞神经网络双周期间歇控制滞后同步

提出了一个时滞神经网络周期间歇控制滞后同步策略,其间歇控制周期为两个不同的周期。利用Lyapunov稳定性理论,证明了时滞神经网络在此控制策略下能够实现同步,并获得了同步解全局指数稳定的充分条件。给出了一个仿真实例验证了控制方案的有效性。     

Stability of Reaction-Diffusion Recurrent Neural Networks with Distributed Delays and Neumann Boundary Conditions on Time Scales

The existence of equilibrium solutions to reaction-diffusion recurrent neural networks with distributed delays and Neumann boundary conditions on time scales is proved by the topological degree theory and M-matrix method. Under some sufficient conditions, we obtain the uniqueness and global exponential stability of equilibrium solution to reaction-diffusion recurrent neural networks with distributed delays and Neumann boundary conditions on time scales by constructing suitable Lyapunov functional and inequality skills. Two examples are given to illustrate the effectiveness of our results.     

Exponential periodicity and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays

In this paper, the exponential periodicity and stability of neural networks with Lipschitz continuous activation functions are investigated, without assuming the boundedness of the activation functions and the differentiability of time-varying delays, as needed in most other papers. The neural networks contain reaction-diffusion terms and both variable and unbounded delays. Some sufficient conditions ensuring the existence and uniqueness of periodic solution and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays are obtained by analytic methods and inequality technique. Furthermore, the exponential converging index is also estimated. The methods, which does not make use of Lyapunov functional, is simple and valid for the periodicity and stability analysis of neural networks with variable and/or unbounded delays. The results extend some previous results. Two examples are given to show the effectiveness of the obtained results.     

Exponential stability of delayed bidirectional associative memory neural networks with reaction diffusion terms

This article considers a class of delayed bi-directional associative memory (BAM) neural networks with reaction diffusion terms and delays. We obtain some simple criteria ensuring the existence and uniqueness of the equilibrium and its global exponential stability by applying homeomorphism mapping, constructing a new Lyapunov functional and inequality techniques. These criteria are independent of delays and posses infinitely adjustable real parameters, which improve and extend some recent results [J. Cao and M. Dong, “Exponential stability of delayed bidirectional associative memory networks”, Appl. Math. Comput., 135, pp. 105–112, 2003; J. Cao and L. Wang, “Exponential stability and periodic oscillatory solution in BAM networks with delays”, IEEE Trans. Neural Networ., 13, pp. 457–463, 2002; Q. Song and J. Cao, “Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms”, Chaos Soliton. Fract., 23, pp. 421–430, 2005.] and have an important instructional significance in the designs and applications of bidirectional associative memory neural networks.     

Exponential stability and periodic oscillatory solution in BAMnetworks with delays

Both exponential stability and periodic oscillatory solution of bidirectional associative memory (BAM) networks with axonal signal transmission delays are considered by constructing suitable Lyapunov functional and some analysis techniques. Some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic oscillatory solutions of BAM with delays. These conditions are presented in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for BAM with delays. In addition, two examples are given to illustrate the results.     

具反映扩散有限连续分布时滞细胞神经网络的全局指数稳定性

研究了具反应扩散有限连续分布细胞神经网络的平衡点的存在性及全局指数稳定性问题,提出了新的比较原理,在对神经元的激励函数的较宽松的条件下,利用同伦不变性原理获得了该系统的平衡点的存在性,利用所得的比较原理获得了该系统全局指数渐近稳定性的充分条件,而且这些条件容易检验,并举了一个数值实例以说明结论的有效性．     

Effect of leakage delay on the almost periodic solutions of fuzzy cellular neural networks

ABSTRACT

In this paper, fuzzy cellular neural networks with time-varying delays in leakage terms are investigated. With the help of the differential inequality theory and almost periodic function theory, a set of sufficient criteria that guarantee the existence and exponential stability of almost periodic solutions of fuzzy cellular neural networks with time-varying delays in leakage terms are established. Our results are new and complement some previously known ones. Moreover, numerical simulations are carried out to verify our theoretical results.     

Global exponential robust stability of reaction–diffusion interval neural networks with continuously distributed delays

This paper considers the existence of the equilibrium point and its global exponential robust stability for reaction-diffusion interval neural networks with variable coefficients and distributed delays by means of the topological degree theory and Lyapunov-functional method. The sufficient conditions on global exponential robust stability established in this paper are easily verifiable. An example is presented to demonstrate the effectiveness and efficiency of our results.     

Global dynamics for non-autonomous reaction-diffusion neural networks with time-varying delays

In this paper, a class of non-autonomous reaction-diffusion neural networks with time-varying delays is considered. Novel methods to study the global dynamical behavior of these systems are proposed. Employing the properties of diffusion operator and the method of delayed inequalities analysis, we investigate global exponential stability, positive invariant sets and global attracting sets of the neural networks under consideration. Furthermore, conditions sufficient for the existence and uniqueness of periodic attractors for periodic neural networks are derived and the existence range of the attractors is estimated. Finally two examples are given to demonstrate the effectiveness of these results.     

Almost periodic solutions for Hopfield neural networks with continuously distributed delays

In this paper Hopfield neural networks with continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this paper are new and they complement previously known results.