Stability of Reaction-Diffusion Recurrent Neural Networks with Distributed Delays and Neumann Boundary Conditions on Time Scales

The existence of equilibrium solutions to reaction-diffusion recurrent neural networks with distributed delays and Neumann boundary conditions on time scales is proved by the topological degree theory and M-matrix method. Under some sufficient conditions, we obtain the uniqueness and global exponential stability of equilibrium solution to reaction-diffusion recurrent neural networks with distributed delays and Neumann boundary conditions on time scales by constructing suitable Lyapunov functional and inequality skills. Two examples are given to illustrate the effectiveness of our results.     

Impulsive Control and Synchronization for Delayed Neural Networks With Reaction–Diffusion Terms

This paper discuss the global exponential stability and synchronization of the delayed reaction–diffusion neural networks with Dirichlet boundary conditions under the impulsive control in terms of $p$-norm and point out the fact that there is no constant equilibrium point other than the origin for the reaction–diffusion neural networks with Dirichlet boundary conditions. Some new and useful conditions dependent on the diffusion coefficients are obtained to guarantee the global exponential stability and synchronization of the addressed neural networks under the impulsive controllers we assumed. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed control methods.      

Global exponential robust stability of reaction–diffusion interval neural networks with continuously distributed delays

This paper considers the existence of the equilibrium point and its global exponential robust stability for reaction-diffusion interval neural networks with variable coefficients and distributed delays by means of the topological degree theory and Lyapunov-functional method. The sufficient conditions on global exponential robust stability established in this paper are easily verifiable. An example is presented to demonstrate the effectiveness and efficiency of our results.     

Robust global exponential stability of Cohen-Grossberg neural networks with time delays

The authors discuss delayed Cohen-Grossberg neural network models and investigate their global exponential stability of the equilibrium point for the systems. A set of sufficient conditions ensuring robust global exponential convergence of the Cohen-Grossberg neural networks with time delays are given.     

Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays

The authors analyze the existence of the equilibrium point and global exponential stability for Hopfield reaction-diffusion neural networks with time-varying delays by means of the topological degree theory and generalized Halanay inequality. Since the diffusion phenomena and time delay could not be ignored in neural networks and electric circuits, the model presented here is close to the actual systems, and the sufficient conditions on global exponential stability established in this paper, which are easily verifiable, have a wider adaptive range.     

Dynamic behaviors of memristor-based delayed recurrent networks

This paper investigates the problem of the existence and global exponential stability of the periodic solution of memristor-based delayed network. Based on the knowledge of memristor and recurrent neural network, the model of the memristor-based recurrent networks is established. Several sufficient conditions are obtained, which ensure the existence of periodic solutions and global exponential stability of the memristor-based delayed recurrent networks. These results ensure global exponential stability of memristor-based network in the sense of Filippov solutions. And, it is convenient to estimate the exponential convergence rates of this network by the results. An illustrative example is given to show the effectiveness of the theoretical results.     

Pseudo Almost Periodic Solution of Recurrent Neural Networks with D Operator on Time Scales

This paper is concerned with a class of neutral type recurrent neural networks with time-varying delays, distributed delay and D operator on time–space scales which unify the continuous-time and the discrete-time recurrent neural networks under the same framework. Some sufficient conditions are given for the existence and the global exponential stability of the pseudo almost periodic solution by using inequality analysis techniques on time scales, fixed point theorem and the theory of calculus on time scales. An example is given to show the effectiveness of the derived results via computer simulations.

     

Improved conditions for global exponential stability of recurrent neural networks with time-varying delays

This paper presents new theoretical results on global exponential stability of recurrent neural networks with bounded activation functions and time-varying delays. The stability conditions depend on external inputs, connection weights, and time delays of recurrent neural networks. Using these results, the global exponential stability of recurrent neural networks can be derived, and the estimated location of the equilibrium point can be obtained. As typical representatives, the Hopfield neural network (HNN) and the cellular neural network (CNN) are examined in detail.     

Novel criteria for global robust exponential stability of neural networks with time-varying delays via LMI approach

The article addresses the problem of global robust exponential stability of interval neural networks with time-varying delays. On the basis of linear matrix inequality technique and M-matrix theory, some novel sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed interval neural networks are presented. It is shown that our results improve and generalize some previously published ones. Some numerical examples and simulations are given to show the effectiveness of the obtained results.     

Exponential stability of stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jumping parameters

In this paper, we investigate the robust exponential stability for stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jump parameters. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain sufficient conditions for the exponential stability of the equilibrium solution. The obtained stability criteria can be easily checked by linear matrix inequality (LMI) techniques. Finally numerical examples are provided to illustrate the obtained theoretical result.     

Delay-independent stability of stochastic reaction–diffusion neural networks with Dirichlet boundary conditions

This paper deals with the problem of global stability of stochastic reaction–diffusion recurrent neural networks with continuously distributed delays and Dirichlet boundary conditions. The influence of diffusion, noise and continuously distributed delays upon the stability of the concerned system is discussed. New stability conditions are presented by using of Lyapunov method, inequality techniques and stochastic analysis. Under these sufficient conditions, globally exponential stability in the mean square holds, regardless of system delays. The proposed results extend those in the earlier literature and are easier to verify.     

Global robust stability of uncertain delayed neural networks with discontinuous neuron activation

This paper integrates global robust stability of uncertain delay neural networks with discontinuous activation. The activation function is unbounded and the uncertainties are norm bound. By the homotopy invariance and solution properties of the topological degree, the conditions for the existence of equilibrium are given out. Moreover, based on the Lyapunov–Krasovskii stability theory, the conditions of global robust stability for discontinuous delayed neural networks with uncertainties are presented in terms of linear matrix inequality. At last, an illustrative numerical example is provided to show the effectiveness of results given.     

Exponential Synchronization of Stochastic Fuzzy Cellular Neural Networks with Reaction-Diffusion Terms via Periodically Intermittent Control

This paper considers the exponential synchronization of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms based on p-norm. Motivated by the achievements from both the stability of fuzzy cellular neural networks with stochastic perturbation and reaction-diffusion effects and the synchronization issue of coupled chaotic delayed neural networks by using periodically intermittent control approach, a periodically intermittent controller is proposed to guarantee the exponential synchronization of the coupled chaotic neural networks by using Lyapunov stability theory and stochastic analysis approaches. The synchronization results presented in this paper generalize and improve many known results. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme.     

New results concerning the exponential stability of delayed neural networks with impulses

Employing the matrix measure approach and Lyapunov function, the author studies the global exponential stability of delayed neural networks with impulses in this paper. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point for such delayed neural networks with impulses. Finally, three examples are given to show the effectiveness of the results obtained here.     

Global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time-varying delays

In this paper, we present the analytical results on the global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time-varying delays. Sufficient conditions are derived for ascertaining the existence, uniqueness and global exponential periodicity of the oscillatory solution of such recurrent neural networks by using the comparison principle and mixed monotone operator method. The periodicity results extend or improve existing stability results for the class of recurrent neural networks with and without time delays.     

Global Robust Exponential Stability for Interval Delayed Neural Networks with Possibly Unbounded Activation Functions

In this paper, we mainly study the global robust exponential stability of the neural networks with possibly unbounded activation functions. Based on the topological degree theory and Lyapunov functional method, we provide some new sufficient conditions for the global robust exponential stability. Under these conditions, we prove existence, uniqueness and global robust exponential stability of equilibrium point. In the end, some examples are provided to demonstrate the validity of the theoretical results.     

Global robust stability of delayed neural networks with a class of general activation functions

In this paper, the global robust stability is discussed for delayed neural networks with a class of general activation functions. By constructing new Lyapunov functionals, several novel conditions are derived to guarantee the existence, uniqueness and global robust stability of the equilibrium of neural networks with time delays. These conditions do not require the activation functions to be differentiable, bounded or monotonically nondecreasing. The results obtained here are generalizations of some earlier results reported in the literature for neural networks with time delays. In addition, two examples are given to illustrate our proposed results.     

Global dynamics for non-autonomous reaction-diffusion neural networks with time-varying delays

In this paper, a class of non-autonomous reaction-diffusion neural networks with time-varying delays is considered. Novel methods to study the global dynamical behavior of these systems are proposed. Employing the properties of diffusion operator and the method of delayed inequalities analysis, we investigate global exponential stability, positive invariant sets and global attracting sets of the neural networks under consideration. Furthermore, conditions sufficient for the existence and uniqueness of periodic attractors for periodic neural networks are derived and the existence range of the attractors is estimated. Finally two examples are given to demonstrate the effectiveness of these results.     

区间时变细胞神经网络的全局鲁棒指数稳定性

研究了一类区间时变扰动、变时滞细胞神经网络的全局鲁棒指数稳定性问题．利用Leibniz-Newton公式对原系统进行模型变换,并分析了变换模型和原始模型的等价性．基于变换模型,运用线性矩阵不等式的方法,通过选择适当的Lyapunov-Krasovskii泛函,推导了该系统全局鲁棒指数稳定的时滞相关的充分条件．通过数值实例将所得结果与前人的结果相比较,表明了本文所提出的稳定判据具有更低的保守性．     

Impulses-induced exponential stability in recurrent delayed neural networks

The present paper formulates and studies a model of recurrent neural networks with time-varying delays in the presence of impulsive connectivity among the neurons. This model can well describe practical architectures of more realistic neural networks. Some novel yet generic criteria for global exponential stability of such neural networks are derived by establishing an extended Halanay differential inequality on impulsive delayed dynamical systems. The distinctive feature of this work is to address exponential stability issues without a priori stability assumption for the corresponding delayed neural networks without impulses. It is shown that the impulses in neuronal connectivity play an important role in inducing global exponential stability of recurrent delayed neural networks even if it may be unstable or chaotic itself. Furthermore, example and simulation are given to illustrate the practical nature of the novel results.