Synchronization criteria for coupled neural networks with interval time-varying delays and leakage delay

This paper considers the synchronization problem for coupled neural networks with interval time-varying delays and leakage delay. By construction of a suitable Lyapunov-Krasovskii’s functional and utilization of Finsler’s lemma, novel delay-dependent criteria for the synchronization of 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.     

Synchronization conditions for chaotic nonlinear continuous neural networks

This paper deals with the synchronization problem of a class of chaotic nonlinear neural networks. A feedback control gain matrix is derived to achieve the state synchronization of two identical nonlinear neural networks by using the Lyapunov stability theory, and the obtained criterion condition can be verified if a certain Hamiltonian matrix with no eigenvalues on the imaginary axis. The new sufficient condition can avoid solving an algebraic Riccati equation. The results are illustrated through one numerical example.     

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 analysis through coupling mechanism in realistic neural models

Synchronization which relates to the system’s stability is important to many engineering and neural applications. In this paper, an attempt has been made to implement response synchronization using coupling mechanism for a class of nonlinear neural systems. We propose an OPCL (open-plus-closed-loop) coupling method to investigate the synchronization state of driver-response neural systems, and to understand how the behavior of these coupled systems depend on their inner dynamics. We have investigated a general method of coupling for generalized synchronization (GS) in 3D modified spiking and bursting Morris–Lecar (M-L) neural models. We have also presented the synchronized behavior of a network of four bursting Hindmarsh–Rose (H-R) neural oscillators using a bidirectional coupling mechanism. We can extend the coupling scheme to a network of N neural oscillators to reach the desired synchronous state. To make the investigations more promising, we consider another coupling method to a network of H-R oscillators using bidirectional ring type connections and present the effectiveness of the coupling scheme.     

Synchronization for delayed non-autonomous reaction-diffusion fuzzy cellular neural networks

In this letter, the synchronization schemes for delayed non-autonomous reaction-diffusion fuzzy cellular neural networks is considered. Based on the simple adaptive controller, a set of sufficient conditions to guarantee the synchronization are obtained. Moreover, the asymptotic behavior of the unknown parameters can be derived in the meanwhile. At last, some examples are given to show the effectiveness of the main results.     

Synchronization of delayed fuzzy cellular neural networks with impulsive effects

This letter studies synchronization of delayed fuzzy cellular neural networks with impulses and all the parameters unknown. To avoid the difficulties which may be brought by the impulses, a non-impulsive system is used to replaced the system with impulses. Then by the well known Lyapunov–Lasall principle, some new stability criteria are obtained. An example and its simulation were given to illustrate the simpleness and effectiveness of our main results.     

Synchronization of delayed coupled reaction‐diffusion systems on networks

In this paper, the exponential synchronization problem of delayed coupled reaction‐diffusion systems on networks (DCRDSNs) is investigated. Based on graph theory, a systematic method is designed to achieve exponential synchronization between two DCRDSNs by constructing a global Lyapunov function for error system. Two different kinds of sufficient synchronization criteria are derived in the form of Lyapunov functions and coefficients of drive‐response systems, respectively. Finally, a numerical example is given to show the usefulness of the proposed criteria. Copyright © 2014 John Wiley & Sons, Ltd.     

Approximation by neural networks and learning theory

We consider the problem of Learning Neural Networks from samples. The sample size which is sufficient for obtaining the almost-optimal stochastic approximation of function classes is obtained. In the terms of the accuracy confidence function, we show that the least-squares estimator is almost-optimal for the problem. These results can be used to solve Smale's network problem.     

混沌时滞随机神经网络同步控制

研究了一类混沌时滞随机神经网络同步控制问题．采用更具一般性的时滞反馈控制器,通过巧妙地构造Lyapunov数,分别得到了均方指数同步和均方渐近同步两个判别准则．仿真例子表明,新准则是有效的．     

Synchronization of switched neural networks with mixed delays via impulsive control

This paper concerns the problem of global exponential synchronization for a class of switched neural networks with time-varying delays and unbounded distributed delays via impulsive control method. By using Lyapunov stability theory, new synchronization criterion is derived. In our synchronization criterion, the switching law can be arbitrary and the concept of average impulsive interval is utilized such that the obtained synchronization criterion is less conservative than those based on maximum of impulsive intervals. Numerical simulations are given to show the effectiveness and less conservativeness of the theoretical 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.     

Max—min神经网络的一种有效学习算法

本文在Ａ．Ｂｌａｎｃｏ等人的算法的基础上，提出了ｍａｘ－ｍｉｎ神经网络的一种改进了的反馈学习算法，严格证明了该算法的迭代收敛性，理论分析及实例计算结果均表明，本文算法具有算法简单，收敛速度快，输出误差小等显著特点。     

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     

Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control

In this paper, a new method to synchronize two identical chaotic recurrent neural networks is proposed. Using the drive-response concept, a nonlinear feedback control law is derived to achieve the state synchronization of the two identical chaotic neural networks. Furthermore, based on the Lyapunov method, a delay independent sufficient synchronization condition in terms of linear matrix inequality (LMI) is obtained. A numerical example with graphical illustrations is given to illuminate the presented synchronization scheme.     

Specific locking in populations dynamics: Symmetry analysis for coupled heteroclinic cycles

Population dynamics on two sites of ecological fields are studied. Each site shows oscillatory dynamics with a heteroclinic cycle or a limit cycle attractor, and populations migrate between two sites diffusively. In this system, frequency locking states with specific ratios between the oscillations of two sites are observed. The selection of the ratios are explained with the symmetry of the phase space. Other properties of the locking states as behaviors intrinsic to heteroclinic cycles are also discussed.     

Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling

In this paper, the global exponential synchronization is investigated for an array of asymmetric neural networks with time-varying delays and nonlinear coupling, assuming neither the differentiability for time-varying delays nor the symmetry for the inner coupling matrices. By employing a new Lyapunov-Krasovskii functional, applying the theory of Kronecker product of matrices and the technique of linear matrix inequality (LMI), a delay-dependent sufficient condition in LMIs form for checking global exponential synchronization is obtained. The proposed result generalizes and improves the earlier publications. An example with chaotic nodes is given to show the effectiveness of the obtained result.     

Tidal level forecasting using functional and sequential learning neural networks

Prediction of tides is very much essential for human activities and to reduce the construction cost in marine environment. This paper presents two methods (1) an application of the functional networks (FN) and (2) sequential learning neural network (SLNN) procedures for the accurate prediction of tides using very short-term observation. This functional network model predicts the time series data of hourly tides directly while using an efficient learning process by minimizing the error based on the observed data for 30 days. Using the functional network, a very simple equation in the form of finite difference equation using the tidal levels at two previous time steps is arrived at. Sequential learning neural network uses one hidden neuron to predict the current tidal level using the previous four levels quite accurately. Hourly tidal data measured at Taichung harbor and Mirtuor coast along the Taiwan coastal region have been used for testing the functional network and sequential neural network model. Results show that the hourly data on tides for even a month can be predicted efficiently with a very high correlation coefficient.     

Synchronization of neural networks based on parameter identification and via output or state coupling

For neural networks with all the parameters unknown, we focus on the global robust synchronization between two coupled neural networks with time-varying delay that are linearly and unidirectionally coupled. First, we use Lyapunov functionals to establish general theoretical conditions for designing the coupling matrix. Neither symmetry nor negative (positive) definiteness of the coupling matrix are required; under less restrictive conditions, the two coupled chaotic neural networks can achieve global robust synchronization regardless of their initial states. Second, by employing the invariance principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the robust synchronization of almost all kinds of coupled neural networks with time-varying delay based on the parameter identification of uncertain delayed neural networks. Finally, numerical simulations validate the effectiveness and feasibility of the proposed technique.     

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.