More relaxed condition for dynamics of discrete time delayed Hopfield neural networks

The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found. The result obtained holds not only for constant delay but also for time-varying delays.     

Pair-correlated patterns in Hopfield model of neural networks

We study the retrieval properties of the Hopfield model of neural networks when the memorized patterns are statistically correlated in pairs. There is a finite correlationk between the memories of each pair, but memories of different pairs are uncorrelated. The analysis is restricted to the case of an arbitrary but finite number of memories in the thermodynamic limit. We find that there are two retrieval regimes: for 0<T<(1–k) the system recognizes the stored patterns and for (1–k)<T<(1+k) the system is able to recognize pairs, but it is not able to distinguish between its two patterns.     

Synchronization criteria for coupled Hopfield neural networks with time-varying delays

This paper proposes new delay-dependent synchronization criteria for coupled Hopfield neural networks with time-varying delays. By construction of a suitable Lyapunov-Krasovskii's functional and use of Finsler's lemma, novel synchronization criteria for the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique

The global stability problem of Takagi-Sugeno(T-S) fuzzy Hopfield neural networks(FHNNs) with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler’s lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.     

Power law decay of stored pattern stability in sparse Hopfield neural networks

Hopfield neural networks on scale-free networks display the power law relation between the stability of patterns and the number of patterns.The stability is measured by the overlap between the output state and the stored pattern which is presented to a neural network.In simulations the overlap declines to a constant by a power law decay.Here we provide the explanation for the power law behavior through the signal-to-noise ratio analysis.We show that on sparse networks storing a plenty of patterns the stability of stored patterns can be approached by a power law function with the exponent-0.5.There is a difference between analytic and simulation results that the analytic results of overlap decay to 0.The difference exists because the signal and noise term of nodes diverge from the mean-field approach in the sparse finite size networks.     

Exponential stability of delayed Hopfield neural networks with various activation functions and polytopic uncertainties

This Letter deals with the problem of exponential stability for a class of delayed Hopfield neural networks. Based on augmented parameter-dependent Lyapunov-Krasovskii functionals, new delay-dependent conditions for the global exponential stability are obtained for two cases of time-varying delays: the delays are differentiable and have an upper bound of the delay-derivatives, and the delays are bounded but not necessary to be differentiable. The conditions are presented in terms of linear matrix inequalities, which allow to compute simultaneously two bounds that characterize the exponential stability rate of the solution. Numerical examples are included to illustrate the effectiveness of our results.     

Nonlinear H∞ control of structured uncertain stochastic neural networks with discrete and distributed time varying delays

This paper is concerned with the problem of robust H∞ control for structured uncertain stochastic neural networks with both discrete and distributed time varying delays. A sufficient condition is presented for the existence of H∞ control based on the Lyapunov stability theory. The stability criterion is described in terms of linear matrix inequalities （LMIs）, which can be easily checked in practice. An example is provided to demonstrate the effectiveness of the proposed result.     

Stability for delayed reaction–diffusion neural networks

We consider a Hopfield neural network model with diffusive terms, non-decreasing and discontinuous neural activation functions, time-dependent delays and time-periodic coefficients. We provide conditions on interconnection matrices and delays which guarantee that for each periodic input the model has a unique periodic solution that is globally exponentially stable. Even in the case without diffusion, such conditions improve recent results on classical delayed Hopfield neural networks with discontinuous activation functions. Numerical examples illustrate the results.     

混沌神经网络的延时反馈控制研究

针对混沌神经网络，提出了一种改进的延时反馈控制方法. 利用该方法，当延时参数τ为奇数时，被控神经网络收敛于记忆模式以及它的反相模式的2周期上. 若选取不同的延时参数，被控网络则收敛于不同的周期态上. 关键词： 控制混沌 延时反馈控制 混沌神经网络     

Global exponential convergence analysis of delayed cellular neural networks

Some sufficient criteria have been established to ensure the global exponential stability of delayed cellular neural networks by using an approach based on delay differential inequality. Compared with the method of Lyapunov functionals as in most previous studies, our method is simpler and more effective for a stability analysis of delayed system. Some previously established results in the literature are shown to be special cases of the present result.     

Free-matrix-based time-dependent discontinuous Lyapunov functional for synchronization of delayed neural networks with sampled-data control

This paper is concerned with the synchronization of delayed neural networks via sampled-data control. A new technique, namely, the free-matrix-based time-dependent discontinuous Lyapunov functional approach, is adopted in constructing the Lyapunov functional, which takes advantage of the sampling characteristic of sawtooth input delay. Based on this discontinuous Lyapunov functional, some less conservative synchronization criteria are established to ensure that the slave system is synchronous with the master system. The desired sampled-data controller can be obtained through the use of the linear matrix inequality(LMI) technique. Finally, two numerical examples are provided to demonstrate the effectiveness and the improvements of the proposed methods.     

Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks

In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks (DNNs) with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochastic analysis approach and an efficient impulsive delay differential inequality, some new exponential synchronization criteria expressed in the form of the linear matrix inequality (LMI) are derived. The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square, but also can control the exponential synchronization rate. Furthermore, to estimate the stable region of the synchronization error dynamics, a novel optimization control algorithm is proposed, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. Simulation results finally demonstrate the effectiveness of the proposed method.     

Stochastic resonance in Hopfield neural networks for transmitting binary signals

We investigate the stochastic resonance phenomenon in a discrete Hopfield neural network for transmitting binary amplitude modulated signals, wherein the binary information is represented by two stored patterns. Based on the potential energy function and the input binary signal amplitude, the observed stochastic resonance phenomena involve two general noise-improvement mechanisms. A suitable amount of added noise assists or accelerates the switch of the network state vectors to follow input binary signals more correctly, yielding a lower probability of error. Moreover, at a given added noise level, the probability of error can be further reduced by the increase of the number of neurons. When the binary signals are corrupted by external heavy-tailed noise, it is found that the Hopfield neural network with a large number of neurons can outperform the matched filter in the region of low input signal-to-noise ratios per bit.     

Novel delay dependent stability analysis of Takagi—Sugeno fuzzy uncertain neural networks with time varying delays

This paper presents the stability analysis for a class of neural networks with time varying delays that are represented by the Takagi-Sugeno (T-S) model. The main results given here focus on the stability criteria using a new Lyapunov functional. New relaxed conditions and new linear matrix inequality-based designs are proposed that outperform the previous results found in the literature. Numerical examples are provided to show that the achieved conditions are less conservative than the existing ones in the literature.     

基于混沌神经网络的盲检测改进新算法

针对Hopfield神经网络的多起点问题,提出了一种新的基于混沌神经网络的盲信号检测算法,实现了二进制移相键控信号盲检测.据此进一步提出双sigmoid混沌神经网络模型,构造了新的能量函数,且证明了该模型的稳定性,并对网络参数进行配置.仿真实验表明:混沌神经网络能够避免局部极小点且具备较强的抗噪性能,双sigmoid混沌神经网络则继承了其所有的优点,且其收敛速度更快,仅需更短的接收数据即可到达全局真实平衡点,从而降低了算法的计算复杂度,减少了运行时间.     

时滞离散神经网络的同步控制

利用既有效又便于实施的时滞状态反馈控制器,根据所给定的条件构造相应的不等式,研究了带有时滞的离散神经网络模型的同步控制问题,给出了该离散系统指数同步的充分条件.在设计同步控制的时候,没有假设激励函数的有界性、可微性和单调性,给出的条件简便易实施.数值结果进一步证明了该控制方法的有效性. 关键词： 离散神经网络 时滞 同步     

Stability analysis of Markovian jumping stochastic Cohen Grossberg neural networks with discrete and distributed time varying delays

In this paper, the global asymptotic stability problem of Markovian jumping stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays （MJSCGNNs） is considered. A novel LMI-based stability criterion is obtained by constructing a new Lyapunov functional to guarantee the asymptotic stability of MJSCGNNs. Our results can be easily verified and they are also less restrictive than previously known criteria and can be applied to Cohen-Grossberg neural networks, recurrent neural networks, and cellular neural networks. Finally, the proposed stability conditions are demonstrated with numerical examples.     

Synchronization in complex delayed dynamical networks with impulsive effects

The present paper is mainly concerned with the issues of synchronization dynamics of complex delayed dynamical networks with impulsive effects. A general model of complex delayed dynamical networks with impulsive effects is formulated, which can well describe practical architectures of more realistic complex networks related to impulsive effects. Based on impulsive stability theory on delayed dynamical systems, some simple but less conservative criterion are derived for global synchronization of such dynamical network. It is shown that synchronization of the networks is heavily dependent on impulsive effects of connecting configuration in the networks. Furthermore, the theoretical results are applied to a typical SF network composing of impulsive coupled chaotic delayed Hopfield neural network nodes, and are also illustrated by numerical simulations.     

Global exponential stability of mixed discrete and distributively delayed cellular neural network

This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point,then by employing the Lyapunov--Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays,in addition, the example is provided to illustrate the applicability of the result.     

A novel chaotic system with one source and two saddle-foci in Hopfield neural networks

This paper presents the finding of a novel chaotic system with one source and two saddle-foci in a simple three-dimensional (3D) autonomous continuous time Hopfield neural network. In particular, the system with one source and two saddle-foci has a chaotic attractor and a periodic attractor with different initial points, which has rarely been reported in 3D autonomous systems. The complex dynamical behaviours of the system are further investigated by means of a Lyapunov exponent spectrum, phase portraits and bifurcation analysis. By virtue of a result of horseshoe theory in dynamical systems, this paper presents rigorous computer-assisted verifications for the existence of a horseshoe in the system for a certain parameter.