超混沌系统的混合同步控制

基于Lyapunov稳定性理论,提出了一种超混沌系统混合同步控制方法,给出并详细证明了Rossler超混沌系统实现自同步的充分条件以及控制律参数的取值范围,并构建了两个不同结构的Rossler超混沌系统的异结构快速同步的数学模型。数值仿真表明了所设控制器的有效性和方法的可操作性．     

瞬时混沌神经网络的混沌动力学

首先利用"不可分意味着混沌"从理论上证明了一维瞬时混沌神经网络在一定的条件下按Li-Yorke意义是混沌的;特别地,进一步推出了混沌神经网络按Li-Yorke意义是混沌的充分条件,而这将从理论上证明Aihara等人通过数值计算所得结论;最后,为说明前面的结论给出了一个例子及其数值计算的结果。     

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.     

随机时滞神经网络系统的自适应控制稳定性

考查一类具有时滞延迟的随机非自治神经网络系统的两类稳定性问题,不同于常规使用的Lyapunov-Krasovskii函数方法和线性矩阵不等式技巧,通过构造新的比较原则,将神经网络(NNs)与随机神经网络(SNNs)两种模型进行比较,给出了随机神经网络(SNNs)自适应控制器能够使受控系统依概率稳定性和矩稳定性的新的代数判断依据.此外,通过数值算例对主要结果进行验证.     

随机分布参数型Hopfield时滞神经网络的稳定性

基于随机Fubini定理,利用关于空间变量平均的Lyapunov函数与Ito公式,研究了具时滞的分布参数型随机Hopfield神经网络的稳定性与镇定,获得了若干充分条件．     

变时滞随机模糊细胞神经网络稳定性分析(英文)

本文旨在研究一类带变时滞的随机模糊细胞神经网络的稳定性.通过构造恰当的Lyapunov泛函并运用线性矩阵不等式(LMI)理论,作者给出了保证这类神经网络全局渐近稳定的充分条件.本文推导出两个定理:一个用以判定文中模型的全局渐进稳定性,一个用以判定该模型在均方意义下的全局渐近稳定性.     

具有时变时滞和分布时滞随机神经网络p阶矩指数稳定性

在仅要求时滞函数有上界的条件下,运用随机分析理论和微分不等式技巧得到了同时具有时变时滞和分布时滞的随机神经网络的p阶矩指数稳定充分条件,并用具体算例验证了方法的有效性,文章结论推广和改进了相关文献的结果.     

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.     

一类具混合时滞随机神经网络稳定性的推广与应用

将一类具有混合时滞随机神经网络均方渐近稳定的判据推广到不确定神经网络的鲁棒稳定性,所导出的判据都表示为线性矩阵不等式(LMI)的形式,可通过使用一些标准的数值方法求解.最后给出了一个简单的例子说明所提出的判定条件的有效性和可应用性.     

一类随机高阶变时滞神经网络的指数稳定性

对于一类随机高阶变时滞神经网络,应用Brouwer不动点原理和随机分析理论知识,利用Schwarz积分不等式和递推归纳技巧,研究高阶变时滞神经网络在随机扰动下的稳定性,给出其指数稳定判定的充分性条件.最后通过数值例子说明所得结果的有效性.     

Exponential H∞ synchronization for discrete‐time chaotic neural networks with time delays and stochastic perturbations via output feedback control

This paper investigates the problem of exponential H_∞ synchronization of discrete‐time chaotic neural networks with time delays and stochastic perturbations. First, by using the Lyapunov‐Krasovskii (Lyapunov) functional and output feedback controller, we establish the H_∞ performance of exponential synchronization in the mean square of master‐slave systems, which is analyzed using a matrix inequality approach. Second, the parameters of a desired output feedback controller can be achieved by solving a linear matrix inequality. Finally, 2 simulated examples are presented to show the effectiveness of the theoretical results.     

Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method

In this paper, an impulsive controller is designed to achieve the exponential synchronization of chaotic delayed neural networks with stochastic perturbation. By using the impulsive delay differential inequality technique that was established in recent publications, several sufficient conditions ensuring the exponential synchronization of chaotic delayed networks are derived, which can be easily checked by LMI Control Toolbox in Matlab. A numerical example and its simulation is given to demonstrate the effectiveness and advantage of the theory results.     

Synchronization control for the competitive complex networks with time delay and stochastic effects

The synchronization control problem for the competitive complex network with time delay and stochastic effects is investigated by using the stochastic technique and Lyapunov stability theory. The competitive complex network means that the dynamical varying rate of a part of nodes is faster than other nodes. Some synchronization criteria are derived by the full controller and pinning controller, respectively, and these criteria are convenient to be used for concision. A numerical example is provided to illustrate the effectiveness of the method proposed in this paper.     

Finite-time synchronization for coupled systems with time delay and stochastic disturbance under feedback control

This paper proposes a framework for finite-time synchronization of coupled systems with time delay and stochastic disturbance under feedback control. Combining Kirchhoff"s Matrix Tree Theorem with Lyapunov method as well as stochastic analysis techniques, several sufficient conditions are derived. Differing from previous references, the finite time provided by us is related to topological structure of networks. In addition, two concrete applications about stochastic coupled oscillators with time delay and stochastic Lorenz chaotic coupled systems with time delay are presented, respectively. Besides, two synchronization criteria are provided. Ultimately, two numerical examples are given to illustrate the effectiveness and feasibility of the obtained results.     

Quasi-projective synchronization analysis for delayed stochastic quaternion-valued neural networks via state-feedback control strategy

In this paper, we explore the complete synchronization and quasi-projective synchronization in a class of stochastic delayed quaternion-valued neural networks, utilizing a state-feedback control scheme. The studied neural networks into real-valued networks are short of known decomposing, by designing a very general nonlinear controller, according to the quaternion form It\^{o} formula with a number of inequality techniques in the configuration of quaternion domain, we obtained a quasi-projective synchronization criterion for drive-response networks. Moreover, we estimate the error margin for quasi-projective synchronization. At last, the theoretical results are confirmed by a numerical simulation.     

Synchronization of chaotic neural networks with mixed time delays

In this paper, we investigate the synchronization problems of chaotic neural networks with mixed time delays. We first establish the sufficient conditions for synchronization of identical chaotic neural networks with mixed time delays via linear output feedback control. To overcome the difficulty that complete synchronization between nonidentical chaotic neural networks cannot be achieved only by utilizing output feedback control, we use a sliding mode control approach to study the synchronization of nonidentical chaotic neural networks with mixed time delays, where the parameters and functions are mismatched. Numerical simulations are carried out to illustrate the main results.     

Synchronization of chaotic delayed neural networks with impulsive and stochastic perturbations

In this paper, we study the exponential synchronization problem of a class of chaotic delayed neural networks with impulsive and stochastic perturbations. The involved time delays include time-varying delays and unbounded distributed delays. Employing the method of impulsive delay differential inequality, several new sufficient conditions ensuring the exponential synchronization are obtained, which can be easily checked by LMI Control Toolbox in Matlab. Compared with the previous methods, our method does not resort to complicated Lyapunov–Krasovkii, and the results derived are independent of the time-varying delays and do not require the differentiability of delay functions and the monotony of the activation functions. Finally, a numerical example and its simulation is given to show the effectiveness of the obtained results in this paper.     

Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control

-In this paper, we investigate the synchronization problems of chaotic fuzzy cellular neural networks with time-varying delays. To overcome the difficulty that complete synchronization between non-identical chaotic neural networks cannot be achieved only by utilizing output feedback control, we use a sliding mode control approach to study the synchronization of non-identical chaotic fuzzy cellular neural networks with time-varying delays, where the parameters and activation functions are mismatched. This research demonstrates the effectiveness of application in secure communication. Numerical simulations are carried out to illustrate the main results.     

Synchronization of fractional‐order delayed neural networks with hybrid coupling

This article presents new theoretical results on the synchronization for a class of fractional‐order delayed neural networks with hybrid coupling that contains constant coupling and discrete‐delay coupling. This is the first attempt to investigate the synchronization problem of fractional‐order coupled delayed neural networks. Based on the fractional‐order Lyapunov stability theorem and Kronecker product properties, sufficient criteria are established to ensure the fractional‐order coupled neural network to achieve synchronization. Numerical simulations are given to illustrate the correctness of the theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 106–112, 2016     

Exponential stability of hybrid stochastic recurrent neural networks with time-varying delays

In this paper, we consider a class of hybrid Stochastic recurrent neural networks with time-varying delays. By using Razumikhin-type theorem, we not only obtain–almost surely–the exponential stability but also estimate the exponentially convergent rate.