WEIGHTED PSEUDO ALMOST-PERIODIC SOLUTIONS OF SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS WITH MIXED DELAYS

In this paper,we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprising different discrete and distributed time delays.Some sufficient conditions are given for the existence and the global exponential stability of the weighted pseudo almost-periodic solution by employing fixed point theorem and differential inequality techniques.The results of this paper complement the previously known ones.Finally,an illustrative example is given to demonstrate the effectiveness of our results.     

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.     

ADAPTIVE PINNING SYNCHRONIZATION OF COUPLED NEURAL NETWORKS WITH MIXED DELAYS AND VECTOR-FORM STOCHASTIC PERTURBATIONS＊

In this article,we consider the global chaotic synchronization of general coupled neural networks,in which subsystems have both discrete and distributed delays.Stochastic perturbations between subsyste...     

Global exponential stability of fuzzy cellular neural networks with delays and reaction–diffusion terms

In this paper, we study the global exponential stability of fuzzy cellular neural networks with delays and reaction–diffusion terms. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain a sufficient condition for the uniqueness and global exponential stability of the equilibrium solution for a class of fuzzy cellular neural networks with delays and reaction–diffusion terms. The result imposes constraint conditions on the network parameters independently of the delay parameter. The result is also easy to check and plays an important role in the design and application of globally exponentially stable fuzzy neural circuits.     

具有分布时滞耦合神经网络模型的全局同步性分析

本文研究了具分布时滞的神经网络的全局同步性.通过应用Lyapunov泛函和线性矩阵不等式,获得了关于模型全局同步性的几个判定准则,并通过对相关例子进行了数值的仿真,模拟结果与理论分析吻合.     

New conditions for synchronization in complex networks with multiple time-varying delays

In this paper, two kinds of synchronization problems of complex dynamical networks with multiple time-varying delays are investigated, that is, the cases with fixed topology and with switching topology. For the former, different from the commonly used linear matrix inequality (LMI) method, we adopt the approach basing on the scramblingness property of the network’s weighted adjacency matrix. The obtained result implies that the network will achieve exponential synchronization for appropriate communication delays if the network’s weighted adjacency matrix is of scrambling property and the coupling strength is large enough. Note that, our synchronization condition is very new, which would be easy to check in comparison with those previously reported LMIs. Moreover, we extend the result to the case when the interaction topology is switching. The maximal allowable upper bounds of communication delays are obtained in each case. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.     

Weighted pseudo‐almost periodic functions on time scales with applications to cellular neural networks with discrete delays

In this paper, we first propose a concept of weighted pseudo‐almost periodic functions on time scales and study some basic properties of weighted pseudo‐almost periodic functions on time scales. Then, we establish some results about the existence of weighted pseudo‐almost periodic solutions to linear dynamic equations on time scales. Finally, as an application of our results, we study the existence and global exponential stability of weighted pseudo‐almost periodic solutions for a class of cellular neural networks with discrete delays on time scales. The results of this paper are completely new. Copyright © 2016 John Wiley & Sons, Ltd.     

Analysis of global exponential stability and periodic solutions of FCNNs with constant delays and time-varying delays

In this paper, we investigate a class of fuzzy cellular neural networks with constant delays and time-varying delays. By constructing suitable Lyapunov functional and employing Young inequality, we find sufficient conditions for the existence, uniqueness, global exponential stability of equilibrium, and the existence of periodic solutions of fuzzy cellular neural networks with time-varying delays. The results of this paper are new and they extend previously known results.     

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.     

Chaotic synchronization of a fractional-order system based on washout filter control

In this paper, chaos in a fractional-order neural network system with varying time delays is presented, and chaotic synchronization system with varying time delays is constructed. The stability of constructed synchronization system is analyzed by Laplace transformation theory. In addition, the bifurcation graph of the chaotic system is illustrated. The study results show that the chaos in such fractional-order neural networks with varying time delay can be synchronized, and Washout filter control can be used to reduce the range of coupled parameter.     

Adaptive cluster synchronization in networks with time-varying and distributed coupling delays

This paper studies the adaptive cluster synchronization of a generalized linearly coupled network with time-varying delay and distributed delays. This network includes nonidentical nodes displaying different local dynamical behaviors, while for each cluster of that network the internal dynamics is uniform (such as chaotic, periodic, or stable behavior). In particular, the generalized coupling matrix of this network can be asymmetric and weighted. Two different adaptive laws of time-varying coupling strength and a linear feedback control are designed to achieve the cluster synchronization of this network. Some sufficient conditions to ensure the cluster synchronization are obtained by using the invariant principle of functional differential equations and linear matrix inequality (LMI). Numerical simulations verify the efficiency of our proposed adaptive control method.     

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 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.     

Global exponential synchronization of discrete-time high-order switched neural networks and its application to multi-channel audio encryption

For a class of discrete-time high-order switched neural networks with time-varying delays, the global exponential synchronization (GES) problem and its application in audio encryption are addressed. In this work, the state feedback controllers are designed to ensure the GES of response and drive systems, and the controller gains are directly computed by the network parameters. Then, a numerical example is presented to explain the correctness of the synchronization theory. Moreover, a technique to audio encryption/decryption is proposed, and it is applied to a practical example to verify the applicability of the technique. The advantages of this paper are as follows: (i) GES criterion containing a group of simple matrix inequalities is established without the construction of a Lyapunov–Krasovskii functional (LKF), which is not always obvious; (ii) the controller gains are directly represented by the parameters in the network, and then it is easy to apply them to the audio encryption.     

Synchronization schemes for coupled identical Yang–Yang type fuzzy cellular neural networks

This paper proposes an adaptive procedure to the problem of synchronization for a class of coupled identical Yang–Yang type fuzzy cellular neural networks (YYFCNN) with time-varying delays. Based on the simple adaptive controller, a set of sufficient conditions are developed to guarantee the synchronization of the coupled YYFCNN with time-varying delays. The results are much different from previous ones. It is proved that two coupled identical YYFCNN with time-varying delays can achieve synchronization by enhancing the coupled strength dynamically. In addition, this kind of controller is simple to be implemented and it is fairly robust against the effect of weak noise in the given time series. The approaches are based on using the invariance principle of functional differential equations, constructing a general Lyapunov–Krasovskii functional and employing a linear matrix inequality (LMI). An illustrative example and its simulations show the feasibility of our results. Finally, an application is given to show how to apply the presented synchronization scheme of YYFCNN to secure communication.     

Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms

In this paper, the global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms is considered. By establishing an integro-differential inequality with impulsive initial condition and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, several new sufficient conditions are obtained to ensure the global exponential stability of the equilibrium point for fuzzy cellular neural networks with delays and reaction-diffusion terms. These results extend and improve the earlier publications. Two examples are given to illustrate the efficiency of the obtained results.     

Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays

This paper is concerned with the adaptive synchronization problem for a class of stochastic delayed neural networks. Based on the LaSalle invariant principle of stochastic differential delay equations and the stochastic analysis theory as well as the adaptive feedback control technique, a linear matrix inequality approach is developed to derive some novel sufficient conditions achieving complete synchronization of unidirectionally coupled stochastic delayed neural networks. In particular, the synchronization criterion considered in this paper is the globally almost surely asymptotic stability of the error dynamical system, which has seldom been applied to investigate the synchronization problem. Moreover, the delays proposed in this paper are time-varying delays and distributed delays, which have rarely been used to study the synchronization problem for coupled stochastic delayed neural networks. Therefore, the results obtained in this paper are more general and useful than those given in the previous literature. Finally, two numerical examples and their simulations are provided to demonstrate the effectiveness of the theoretical results.     

Stability analysis of Cohen–Grossberg neural network with both time-varying and continuously distributed delays

In this paper, the Cohen–Grossberg neural network model with both time-varying and continuously distributed delays is considered. Without assuming both global Lipschitz conditions on these activation functions and the differentiability on these time-varying delays, applying the idea of vector Lyapunov function, M-matrix theory and inequality technique, several new sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential stability of equilibrium point for Cohen–Grossberg neural network with both time-varying and continuously distributed delays. These results generalize and improve the earlier publications. Two numerical examples are given to show the effectiveness of the obtained results. It is believed that these results are significant and useful for the design and applications of the Cohen–Grossberg neural networks.     

Finite‐time stability of CNNs with neutral proportional delays and time‐varying leakage delays

In this paper, a class of cellular neural networks with neutral proportional delays and time‐varying leakage delays is considered. Some results on the finite‐time stability for the equations are obtained by using the differential inequality technique. In addition, an example with numerical simulations is given to illustrate our results, and the generalized exponential synchronization is also established. Copyright © 2016 John Wiley & Sons, Ltd.     

Global exponential stability of impulsive Cohen–Grossberg neural network with time-varying delays

In this paper, the impulsive Cohen–Grossberg neural network model with time-varying delays is considered. Applying the idea of vector Lyapunov function, M-matrix theory and inequality technique, several new sufficient conditions are obtained to ensure global exponential stability of equilibrium point for impulsive Cohen–Grossberg neural network with time-varying delays. These results generalize a few previous known results and remove some restrictions on the neural network. An example is given to show the effectiveness of the obtained results. It is believed that these results are significant and useful for the design and applications of the Cohen–Grossberg neural network.