带有时滞的Clifford值神经网络的全局指数稳定性

研究了带有离散时滞和分布时滞的Clifford值递归神经网络的全局指数稳定性问题.首先运用M矩阵的性质和不等式技巧证明了Clifford值递归神经网络平衡点的存在性和唯一性;然后通过数学分析方法,得到了Clifford值递归神经网络全局指数稳定的判定条件;最后数值仿真例子验证了获得结果的有效性.     

时滞Hopfield神经网络模型的全局吸引性和全局指数稳定性

对具有时滞的Hopfield神经网络模型,在非线性神经元激励函数是Lipschitz连续(而非已有的大部分文献中假设是Sigmoid函数)的条件下,通过构造适当的泛函,给出了这类模型全局吸引和平衡点全局指数稳定的易于验证的充分条件。     

Exponential stability criteria for discrete-time recurrent neural networks with time-varying delay

In this paper, the robust global exponential stability is investigated for the discrete-time recurrent neural networks (RNNs) with time-varying interval delay. By choosing an augmented Lyapunov–Krasovskii functional, delay-dependent results guaranteeing the global exponential stability and the robust exponential stability of the concerned neural network are obtained. The results are shown to be a generalization of some previous results, and less conservative than the existing works. Two numerical examples are given to demonstrate the applicability of the proposed method.     

Global exponential stability in Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions via LMI approach

In this paper, we study the global exponential stability in a Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions. Based on assuming that the activation functions are neither bounded nor monotonous or differentiable, several algebraic criterions in linear matrix inequality form for the global exponential stability in a Lagrange sense of the neural networks are obtained by virtue of Lyapunov functions and Halanay delay differential inequality. Meanwhile, the estimations of the globally exponentially attractive sets are given out. The results derived here are more general than that of the existing reference. Finally, two examples are given and analyzed to demonstrate our results.     

变时滞Hopfield神经网络的全局吸引性和全局指数稳定性

对一类具时滞的Hopfeild型神经网络模型,在非线性神经元激励函数只要求满足Lipschitz连续的条件下,利用推广的Halanay时延微分析不等式、Dini导数以及泛函微分析技术,给出了这类模型的平衡点全局指数稳定性和全局吸引性的充分条件,这些条件易于检验,且改进和推广了前人的结论.此外,此文给出了研究神经网络模型的全局吸引性的微分不等式比较方法.     

Stability in Lagrange sense for Cohen–Grossberg neural networks with time-varying delays and finite distributed delays

In this paper, we study the global exponential stability in Lagrange sense for a class of Cohen–Grossberg neural networks with time-varying delays and finite distributed delays. Based on the Lyapunov stability theory, several global exponential attractive sets in which all trajectories converge are obtained. We analyze three different types of activation functions which include both bounded and unbounded activation functions. These results can also be applied to analyze monostable as well as multistable and more extensive neural networks due to making no assumptions on the number of equilibria. Meanwhile, the results obtained in this paper are more general and challenging than that of the existing references. Finally, one example is given and analyzed to verify our results.     

Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations

This paper investigates the dynamics of a class of recurrent neural networks where the neural activations are modeled by discontinuous functions. Without presuming the boundedness of activation functions, the sufficient conditions to ensure the existence, uniqueness, global exponential stability and global convergence of state equilibrium point and output equilibrium point are derived, respectively. Furthermore, under certain conditions we prove that the system is convergent globally in finite time. The analysis in the paper is based on the properties of M-matrix, Lyapunov-like approach, and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. The obtained results extend previous works on global stability of recurrent neural networks with not only Lipschitz continuous but also discontinuous neural activation functions.     

一类具分布时滞神经网络的全局指数稳定性

本文讨论了一类具分布时滞神经网络的稳定性.利用广义Dahlquist数和广义Halanay不等式,我们得到了该神经网络平衡点存在、唯一且全局指数稳定的充分条件.此外,我们的方法还估计出了神经网络指数收敛到平衡点的速度.由于我们的方法去除了关于激活函数的有界性、可微性和单调性的常用假设,因此我们的结果是某些现有结果的推广和改进.     

变时滞BAM神经网络的全局指数稳定性

研究一类变时滞BAM神经网络平衡点的全局指数稳定性问题.在不要求激励函数全局Lipschitz条件下,通过构造合适的Lyapunov泛函,并结合Young不等式,得到了BAM神经网络模型在一定条件下全局指数稳定的一些充分条件,推广和改进了前人的相关结论,为综合设计指数稳定的时滞BAM神经网络提供了依据.     

SCALE-TYPE STABILITY FOR NEURAL NETWORKS WITH UNBOUNDED TIME-VARYING DELAYS

This paper studies scale-type stability for neural networks with unbounded time-varying delays and Lipschitz continuous activation functions. Several sufficient conditions for the global exponential stability and global asymptotic stability of such neural networks on time scales are derived. The new results can extend the existing relevant stability results in the previous literatures to cover some general neural networks.     

BAM-type impulsive neural networks with time-varying delays

By using the continuation theorem of coincidence degree theory and constructing a suitable Lyapunov functional, we derive some sufficient conditions for the existence and global exponential stability of a unique periodic solution of BAM neural networks, which assumes neither the monotony nor the boundedness of the activation functions. It is believed that these results are significant and useful for the design and applications of BAM neural networks.     

含分布时滞递归神经网络的一般衰减同步

对具有分布时滞的递归神经网络模型进行了研究,并通过构造适当的Lyapunov-Krasovskii函数和非线性控制函数,采用不等式估计方法,得到了所研究模型一般衰减同步的充分条件.最后给出了一个例子,进一步说明了所得结论的正确性.     

Stability analysis in Lagrange sense for a non-autonomous Cohen–Grossberg neural network with mixed delays

The paper discusses the global exponential stability in the Lagrange sense for a non-autonomous Cohen–Grossberg neural network (CGNN) with time-varying and distributed delays. The boundedness and global exponential attractivity of non-autonomous CGNN with time-varying and distributed delays are investigated by constructing appropriate Lyapunov-like functions. Moreover, we provide verifiable criteria on the basis of considering three different types of activation function, which include both bounded and unbounded activation functions. These results can be applied to analyze monostable as well as multistable biology neural networks due to making no assumptions on the number of equilibria. Meanwhile, the results obtained in this paper are more general and challenging than that of the existing references. In the end, an illustrative example is given to verify our results.     

New results on input-to-state convergence for recurrent neural networks with variable inputs

In this paper, we study a class of recurrent neural networks (RNNs) arising from optimization problems. By constructing appropriate Lyapunov functions, we prove two new results on input-to-state convergence of RNNs with variable inputs. Numerical simulations are also given to demonstrate the convergence of the solutions.     

Exponential stability of recurrent neural networks with time-varying discrete and distributed delays

This paper is concerned with the problems of determining the global exponential stability and estimating the exponential-convergence rate for a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. By constructing an appropriate Lyapunov–Krasovskii functional and employing linear matrix inequality (LMI) technique, new delay-dependent exponential-stability criteria are derived in term of LMIs and the exponential-convergence rate is estimated. Numerical examples are given to show the effectiveness and improvement of the obtained results.     

New results of global robust exponential stability of neural networks with delays

In this paper, the global robust exponential stability of interval neural networks with delays is investigated. Employing homeomorphism techniques and Lyapunov functions, we establish some sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed neural networks. It is shown that the obtained results improve and generalize the previously published results.     

Positive invariant sets and global exponential attractive sets of a class of neural networks with unbounded time-delays

In this paper, we study the positive invariant sets and global exponential attractive sets for a class of neural networks with unbounded time-delays. Based on the assumption for the activation function satisfying the global Lipschitz condition, several algebraic criterions for the aforementioned sets are obtained by constructing proper Lyapunov functions and employing Young inequality. Finally, examples are given and analyzed to demonstrate our results.     

一类变时滞神经网络的全局指数稳定性

本文研究一类变时滞神经网络平衡点的全局指数稳定性.在不要求激活函数全局Lipschitz条件下,利用Lyapunov函数方法,并结合Young不等式和Halanay时滞微分不等式,得到了系统全局指数稳定的充分条件.文末,一个数值例子用以说明本文结果的有效性.     

Exponential stability of impulsive high-order cellular neural networks with time-varying delays

The paper considers the problems of global exponential stability for impulsive high-order neural networks with time-varying delays. By employing the Hardy inequality and the Lyapunov functional method, we present some new criteria ensuring exponential stability. The activation functions are not assumed to be differentiable or strictly increasing, and no assumption on the symmetry of the connection matrices is necessary. These criteria are important in signal processing and the design of networks. Moreover, we also extend the previously known results. One illustrative example is also given in the end of this paper to show the effectiveness of our results.     

Towards a unified recurrent neural network theory: The uniformly pseudo-projection-anti-monotone net

In the past decades, various neural network models have been developed for modeling the behavior of human brain or performing problem-solving through simulating the behavior of human brain. The recurrent neural networks are the type of neural networks to model or simulate associative memory behavior of human being. A recurrent neural network (RNN) can be generally formalized as a dynamic system associated with two fundamental operators: one is the nonlinear activation operator deduced from the input-output properties of the involved neurons, and the other is the synaptic connections (a matrix) among the neurons. Through carefully examining properties of various activation functions used, we introduce a novel type of monotone operators, the uniformly pseudo-projectionanti-monotone (UPPAM) operators, to unify the various RNN models appeared in the literature. We develop a unified encoding and stability theory for the UPPAM network model when the time is discrete. The established model and theory not only unify but also jointly generalize the most known results of RNNs. The approach has lunched a visible step towards establishment of a unified mathematical theory of recurrent neural networks.