Nonlinear Lipschitz measure and adaptive control for stability and synchronization in delayed inertial Cohen‐Grossberg–type neural networks

In this paper, without transforming the original inertial neural networks into the first‐order differential equation by some variable substitutions, time‐varying delays are introduced into inertial Cohen‐Grossberg–type networks and the existence, the uniqueness, and the asymptotic stability and synchronisation for the neural networks are investigated. Firstly, the existence of a unique equilibrium point is proved by using nonlinear Lipschitz measure method. Second, by finding a new Lyapunov‐Krasovskii functional, some sufficient conditions are derived to ensure the asymptotic stability, the asymptotic synchronization, and the asymptotic adaptive synchronization. The results of this paper are new and they complete previously known results. We illustrate the effectiveness of the approach through a few examples.     

Global stability analysis of bidirectional associative memory neural networks with time delay

In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, we present new conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of bidirectional associative memory neural networks with fixed time delays or distributed time delays. The results are applicable to both symmetric and non‐symmetric interconnection matrices, and all continuous non‐monotonic neuron activation functions. Copyright © 2001 John Wiley & Sons, Ltd.     

Absolutely exponential stability in delayed cellular neural networks

In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, we present a necessary and sufficient condition ensuring the existence and uniqueness of the equilibrium point of cellular neural network with fixed time delays (DCNNs). Using M‐matrix theory, Liapunov functionals and functions are constructed and employed to establish sufficient conditions for absolutely exponential stability of DCNNs. The results are applicable to DCNNs with both symmetric and non‐symmetric interconnection matrices, and globally Lipschitz continuous activation functions. Copyright © 2002 John Wiley & Sons, Ltd.     

Novel stability criteria of Cohen–Grossberg neural networks with time‐varying delays

In this paper, a class of Cohen–Grossberg neural networks with time‐varying delays is investigated. Based on several new Lyapunov–Krasovskii functionals, by employing the homeomorphism mapping principle, the Halanay inequality, a nonlinear measure approach and linear matrix inequality techniques, several delay‐independent sufficient criteria are obtained for the existence, uniqueness and globally exponential stability of considered neural networks. Without assuming the boundedness and monotonicity of activation functions, the obtained conditions generalize some previous results in the literature. Two examples are also given to show the less conservativeness of the obtained conditions. Copyright © 2010 John Wiley & Sons, Ltd.     

Stability analysis of delayed fuzzy Cohen-Grossberg neural networks with discontinuous activations

In this article, we investigate the dynamical behavior of a class of delayed fuzzy Cohen-Grossberg neural networks (FCGNNs) with discontinuous activation functions subject to time delays and fuzzy terms. By using the inequality analysis technique and the M-matrix theory, sufficient and proper conditions are given in order to establish the existence, convergence, and global exponential stability of equilibrium point of the system. In particular, we discuss the impact of discontinuous neuron activations on the existence and exponential stability of equilibrium point for FCGNNs. Two numerical examples are provided to substantiate the theoretical results.     

Equilibrium analysis of non-symmetric CNNs

Two useful results concerning the equilibrium analysis of non-symmetric cellular neural networks (CNNs) are presented. First a new sufficient condition ensuring the existence of a stable equilibrium point in the total saturation region is given. Then another condition which guarantees the uniqueness and global asymptotic stability of the equilibrium point is obtained.     

Exponential stability of impulsive Cohen–Grossberg networks with distributed delays

In this paper, we investigate impulsive Cohen–Grossberg networks with distributed delays. By Lyapunov–Kravsovskii functional and homeomorphism theory, some new sufficient conditions are established for the existence and global exponential stability of a unique equilibrium without strict conditions imposed on self‐regulation functions. The obtained sufficient conditions are easy to verify, meanwhile we remove the usual assumption that the activation functions are bounded and our results improve the previously known results. It is believed that these results are significant and useful for the design and applications of Cohen–Grossberg networks. Copyright © 2007 John Wiley & Sons, Ltd.     

On global asymptotic stability for a class of delayed neural networks

This paper deals with the problem of stability analysis for a class of delayed neural networks described by nonlinear delay differential equations of the neutral type. A new and simple sufficient condition guaranteeing the existence, uniqueness and global asymptotic stability of an equilibrium point of such a kind of delayed neural networks is developed by the Lyapunov–Krasovskii method. The condition is expressed in terms of a linear matrix inequality, and thus can be checked easily by recently developed standard algorithms. When the stability condition is applied to the more commonly encountered delayed neural networks, it is shown that our result can be less conservative. Examples are provided to demonstrate the effectiveness of the proposed criteria. Copyright © 2011 John Wiley & Sons, Ltd.     

Global exponential stability of antiperiodic solutions for impulsive discrete‐time Markovian jumping stochastic BAM neural networks with additive time‐varying delays and leakage delay

This paper presents a global exponential stability of antiperiodic solution for a class of impulsive discrete‐time Markovian jumping stochastic bidirectional associative memory neural networks with additive time‐varying delays and leakage delay. By utilizing the Lyapunov‐Krasovskii functional and contraction mapping principle, several sufficient conditions and linear matrix inequalities are derived for verifying globally exponentially stable in the mean square. There is a new delay‐dependent criterion for checking the existence, uniqueness, and global stability for antiperiodic solution. Meantime, by using the numerically efficient MATLAB Toolbox, simulation examples are offered to show the effectiveness and usefulness of the obtained result.     

非对称细胞神经网络稳定平衡点的存在性

利用饱和域的特性,和拟对角列支配矩阵与M-矩阵之间的关系,获得了非对称细胞神经网络(简称CNNS)的稳定平衡点存在的两个充分条件;在此基础上,通过定义一个更高阶的神经网络模型,推广了该网络存在稳定平衡点的结果;通过大量的模拟仿真,提出了非对称细胞神经网络完全稳定的充分条件,并就二细胞神经网络的情况给予了证明;最后,将本文的结果与已取得的结果进行了比较,并给出一个实例说明本文取得的结果优于已有文献取得的结果.     

Finite‐time synchronization and adaptive synchronization of memristive recurrent neural networks with delays

This paper solves the finite‐time synchronization and adaptive synchronization problems of drive‐response memristive recurrent neural networks with delays under two control methods. First, the state‐feedback control rule containing delays and the adaptive control rule are designed for realizing synchronization of drive‐response memristive recurrent neural networks in finite time. Then, on the basis of the Lyapunov stability theory, many algebraic sufficient conditions are obtained to guarantee finite‐time synchronization and adaptive synchronization of drive‐response memristive recurrent neural networks via two control methods, which are easily verified. In addition, the estimation of the upper bounds of the settling time of finite‐time synchronization is obtained. Lastly, to illustrate the effectiveness of the obtained theoretical results, two examples are given.     

Novel stability criteria for bidirectional associative memory neural networks with time delays

In this paper, the bidirectional associative memory (BAM) neural network with axonal signal transmission delay is considered. This model is also referred to as a delayed dynamic BAM model. By combining a number of different Lyapunov functionals with the Razumikhin technique, some sufficient conditions for the existence of a unique equilibrium and global asymptotic stability of the network are derived. These results are fairly general and can be easily verified. Besides, the approach for the analysis allows one to consider several different types of activation functions, including piecewise linear sigmoids with bounded activations as well as C¹‐smooth sigmoids. It is believed that these results are significant and convenient in the design and applications of BAM neural networks. Copyright © 2002 John Wiley & Sons, Ltd.     

Robust control of delayed Cohen–Grossberg neural networks

In this paper, robust control of Cohen–Grossberg neural networks with time delays is considered based on Lyapunov functional method and matrix inequality technique. Several new controllers with time delays and without time delays are designed to ensure the global asymptotic stability of equilibrium point, respectively. Finally, simulation examples are constructed to justify the proposed theoretical analysis. Copyright © 2007 John Wiley & Sons, Ltd.     

Global exponential stability of a class of impulsive cellular neural networks with supremums

In this paper, we study the problem of global exponential stability for impulsive cellular neural networks with time‐varying delays and supremums. Using Young's inequality and Lyapunov‐like functions, new stability criteria are proved. Because supremums and impulses are relevant in various contexts, including problems in the theory of automatic control, our results can be applied in the qualitative investigations of many practical problems of diverse interest. Copyright © 2013 John Wiley & Sons, Ltd.     

Effects of leakage delay on global asymptotic stability of complex‐valued neural networks with interval time‐varying delays via new complex‐valued Jensen's inequality

This paper investigates the global asymptotic stability analysis for a class of complex‐valued neural networks with leakage delay and interval time‐varying delays. Different from previous literature, some sufficient information on a complex‐valued neuron activation function and interval time‐varying delays has been considered into the record. A suitable Lyapunov‐Krasovskii functional with some delay‐dependent terms is constructed. By applying modern integral inequalities, several sufficient conditions are obtained to guarantee the global asymptotic stability of the addressed system model. All the proposed criteria are formulated in the structure of a complex‐valued linear matrix inequalities technique, which can be checked effortlessly by applying the YALMIP toolbox in MATLAB linear matrix inequality. Finally, two numerical examples with simulation results have been provided to demonstrate the efficiency of the proposed method.     

Convergence analysis of general neural networks under almost periodic stimuli

In this paper, we investigate the convergence dynamics of 2^N almost periodic encoded patterns of general neural networks subjected to external almost periodic stimuli, including almost periodic delays. Invariant regions are established for the existence of 2^N almost periodic encoded patterns under two classes of activation functions. By employing the property of ??‐cone and inequality technique, attracting basins are estimated and some criteria are derived for the networks to converge exponentially toward 2^N almost periodic encoded patterns. The results obtained are new; they extend and generalize the corresponding results existing in the previous literature. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust stochastic convergence and stability of neutral‐type neural networks with Markovian jump and mixed delays

The robust stochastic convergence and stability in mean square are investigated for a class of uncertain neutral‐type neural networks with both Markovian jump parameters and mixed delays. First, by employing the Lyapunov method and a generalized Halanay‐type inequality for stochastic differential equations, a delay‐dependent condition is derived to guarantee the state variables of the discussed neural networks to be globally uniformly exponentially stochastic convergent to a ball in the state space with a prespecified convergence rate. Next, by applying the Jensen integral inequality and a novel reciprocal convex lemma, a delay‐dependent criterion is developed to achieve the globally robust stochastic stability in mean square. With some parameters being fixed in advance, the proposed conditions are all expressed in terms of LMIs, which can be solved numerically by employing the standard MATLAB LMI toolbox package. Finally, two illustrated examples are given to show the effectiveness and less conservatism of the obtained results over some existing works. Copyright © 2014 John Wiley & Sons, Ltd.     

Comparative analysis on Hopf bifurcation of integer-order and fractional-order two-neuron neural networks with delay

This article mainly focuses on the stability and the existence of Hopf bifurcation of integer-order and fractional-order two-neuron neural networks with delay. First of all, we obtain the sufficient criterion to ensure the stability and the existence of Hopf bifurcation of integer-order two-neuron neural networks with delay. Next, we establish the sufficient condition guaranteeing the stability and the existence of Hopf bifurcation of fractional-order two-neuron neural networks with delay. The study reveals that the time delay has a vital effect on the stability and Hopf bifurcation of integer-order and fractional-order two-neuron neural networks with delay. By comparative analysis on Hopf bifurcation for integer-order and fractional-order two-neuron neural networks with delay, we find that under an appropriate parameter conditions, the stability region can be enlarged, and the time of appearance of Hopf bifurcation of the involved two-neuron neural networks can be postponed by using fractional-order case. Finally, computer simulation results are presented to illustrate the theoretical findings. The established results of this article play an important role in designing and controlling networks.     

基于动态博弈的电力市场均衡的稳定性分析

对电力市场中的重复拍卖,用动态博弈的方法,以电价为参考变量,利用Betrand模型重点研究了Pool模式下纯策略Nash均衡点的唯一性与稳定性,以及Nash均衡的收敛性质。研究结果表明,均衡点的稳定性与发电容量必须运行率（MRR）以及由MRR决定的均衡点的个数关系密切,当均衡点唯一时必然稳定;存在多个均衡点时均衡点的稳定性与市场初始状态有关。文中采用了全局稳定、区域稳定、随机状态、等效边际成本等概念来更好地说明电力市场中的问题,并且用图形的方法直观地对均衡点的稳定性问题做出了描述。