变时滞细胞神经网络稳定性分析

利用矩阵测度、Liapunov函数和Halanay时滞不等式的方法研究了具有变时滞的细胞神经网络模型平衡点的全局指数稳定性问题.给出了判定平衡点全局指数稳定性的几个代数判据,可用于时滞细胞神经网络的设计与检验,数值算例说明其结果的优越性.     

变时滞细胞神经网络的全局指数稳定性研究

本文采用Lyapunov-Krasovskii泛函方法对一类变时滞细胞神经网络的全局指数稳定性进行了研究,得出了一些关于DCNN全局指数稳定性的充分条件。     

随机变时滞模糊神经网络的均方指数稳定性

利用Lyapunov泛函和随机分析的方法,研究了一类具有变时滞随机模糊细胞神经网络的均方指数稳定性,得到了这类神经网络均方指数稳定性的充分条件.数值例子说明了得到的结果的有效性.     

具无限变时滞的神经网络的稳定性分析

本文研究了具无限变时滞的神经网络的全局指数稳定性，在假设神经元输出输入活化函数有界和满足全局Lipschitz条件下，得到了神经网络具唯一平衡点且该平衡点全局指数稳定的一些充分条件，推广了已有文献中无时滞的相应结果。     

随机扰动神经网络的脉冲控制

脉冲控制具有响应速度快,鲁棒性和抗干扰能力好的特点,被广泛应用于参数随机扰动的动力学系统的控制.本文研究一类参数随机扰动的变时滞细胞神经网络在脉冲控制下的全局指数稳定性问题.利用Ly印unov稳定性理论和离散Halanay不等式技术手段,分别给出在脉冲控制下,参数随机扰动和无参数扰动的变时滞细胞神经网络全局指数稳定的充分条件.最后,通过数值算例说明所得结果.     

细胞神经网络的指数稳定性

该文研究了具有可变时滞的随机细胞神经网络的指数 稳定性,应用Razumikhin定理与Lyapunov函数,建立了这种细胞神经网络均方指数稳定与几乎必然指数稳定的两类判据,一类是时滞无关而另一类是时滞相关.     

高阶变时滞广义细胞神经网络的全局指数周期性

研究了高阶变时滞广义细胞神经网络的全局指数周期性.引入可调参数和通过构造合适的Lyapunov泛函并利用Brouwer压缩映象原理,得到了神经网络周期解存在唯一且全局指数周期与全局指数稳定的充分条件,并给出一个例子说明结论的有效性.     

时滞细胞神经网络的时滞相关指数稳定性

应用Lyapunov泛函法研究了具有时滞的细胞神经网络（DCNNs）的平衡点的全局指数稳定性，获得了一个指数稳定性的判定准则。这个准则与时滞的大小有关，即DCNNs是指数稳定的只要系统所含时滞不超过一个界。     

具有时滞的细胞神经网络周期解与稳定性

本文研究了具有时滞的细胞神经网络周期解存在性和平凡解的稳定性问题 .利用 Lyapunov函数法并结合不等式分析技巧 ,我们首先证明了时滞细胞神经网络的解是有界的 ,然后建立了时滞细胞神经网络的周期解的存在准则 ,最后在时滞细胞神经网络有平衡点时 ,给出了神经网络系统的平衡点指数稳定的充分条件 .其结果推广了文 [7,8]的相应结果 .     

具比例时滞高阶广义细胞神经网络的全局指数周期性

研究了一类具比例时滞高阶广义细胞神经网络的全局指数周期性与稳定性问题.通过非线性变换y_i(t)=x_i(e~t),将一类具比例时滞高阶广义细胞神经网络等价地变换成一类具常时滞与时变系数的高阶广义细胞神经网络,再通过构造合适的Lyapunov泛函,利用Brouwer压缩映象原理和一些不等式的分析技巧,得到了该神经网络的周期解的存在唯一且全局指数周期与全局指数稳定的几个新的时滞依赖的充分条件,并且这些条件仅通过一些简单的代数运算就容易验证.     

Global exponential stability of fuzzy cellular neural networks with delays and reaction–diffusion terms

In this paper, we study the global exponential stability of fuzzy cellular neural networks with delays and reaction–diffusion terms. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain a sufficient condition for the uniqueness and global exponential stability of the equilibrium solution for a class of fuzzy cellular neural networks with delays and reaction–diffusion terms. The result imposes constraint conditions on the network parameters independently of the delay parameter. The result is also easy to check and plays an important role in the design and application of globally exponentially stable fuzzy neural circuits.     

具有脉冲和无限时滞的模糊细胞神经网络的全局指数稳定性

本文讨论了具有脉冲和无限时滞的模糊细胞神经网络的全局指数稳定性.通过建立一个脉冲时滞%积分微分不等式,以及模糊逻辑算子与M-矩阵的性质,不仅得到了系统全局指数稳定的充分条件,而且也给出了指数收敛速度.最后,所给的例子充分验证了文中所给出的充分条件的有效性.     

具有脉冲和无限时滞的模糊细胞神经网络的全局指数稳定性

In this paper,the global exponential stability of fuzzy cellular neural networks with impulses and infinite delays is investigated.Based on an impulsive delayed integro-differential inequality and the properties of fuzzy logic operation and M-matrix,an easily verified sufficient condition is obtained.Moreover,the exponential convergent rate for the fuzzy cellular neural networks with impulses and infinite delays is also given.An example is given to illustrate the effectiveness of our theoretical result.     

Exponential stability and periodic solution for fuzzy BAM Neural networks with time varying delays

In this paper, a class of fuzzy BAM neural networks with time varying delays is discussed. By using the properties of M-matrix, Linear Matrix Inequality（LMI） approach and general Lyapunov-Krasovskii functional, some new sufficient conditions are derived to ensure the existence of periodic solutions and the global exponential stability of the fuzzy BAM neural networks with time varying delays. These results have important significance in the design of global exponential stable BAM networks with delays. Moreover, an example is given to illustrate that the conditions of the results in the paper are feasible.     

变时滞随机Cohen-Grossberg神经网络的几乎肯定指数稳定性

通过构造Lyapunov泛函、利用半鞅收敛定理得到了变时滞随机Cohen-Grossberg神经网络几乎肯定指数稳定的判别准则.     

Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms

In this paper, the global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms is considered. By establishing an integro-differential inequality with impulsive initial condition and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, several new sufficient conditions are obtained to ensure the global exponential stability of the equilibrium point for fuzzy cellular neural networks with delays and reaction-diffusion terms. These results extend and improve the earlier publications. Two examples are given to illustrate the efficiency of the obtained results.     

Finite‐time stability of CNNs with neutral proportional delays and time‐varying leakage delays

In this paper, a class of cellular neural networks with neutral proportional delays and time‐varying leakage delays is considered. Some results on the finite‐time stability for the equations are obtained by using the differential inequality technique. In addition, an example with numerical simulations is given to illustrate our results, and the generalized exponential synchronization is also established. Copyright © 2016 John Wiley & Sons, Ltd.     

Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple discrete and distributed time-varying delays

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the stability analysis for stochastic cellular neural networks with multiple discrete and distributed time varying delays. A novel linear matrix inequality (LMI) based stability criterion is derived to guarantee the asymptotic stability of stochastic cellular neural networks with multiple discrete and distributed time varying delays which are represented by T–S fuzzy models. The derived delay-dependent stability conditions are based on free-weighting matrices method, Lyapunov stability theory and LMI technique. In fact, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. The delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay is removed. Our results can be specialized to several cases including those studied extensively in the literature. Finally, numerical examples are given to demonstrate the effectiveness and conservativeness of our results.     

Analysis of global exponential stability and periodic solutions of FCNNs with constant delays and time-varying delays

In this paper, we investigate a class of fuzzy cellular neural networks with constant delays and time-varying delays. By constructing suitable Lyapunov functional and employing Young inequality, we find sufficient conditions for the existence, uniqueness, global exponential stability of equilibrium, and the existence of periodic solutions of fuzzy cellular neural networks with time-varying delays. The results of this paper are new and they extend previously known results.     

Global asymptotic stability of CNNs with impulses and multi‐proportional delays

This paper is devoted to global asymptotic stability of cellular neural networks with impulses and multi‐proportional delays. First, by means of the transformation v_i(t) = u_i(e^t), the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Second, we prove the global exponential stability of the latter by nonlinear measure, and that the exponential stability of the latter implies the asymptotic stability of the former. We furthermore provide a sufficient condition to the existence, uniqueness, and the global asymptotic stability of the equilibrium point of the former. Our results are generalizations of some existing ones. Finally, an example and its simulation are presented to illustrate effectiveness of our method. Copyright © 2015 John Wiley & Sons, Ltd.