Almost periodic solutions for Hopfield neural networks with continuously distributed delays

In this paper Hopfield neural networks with continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this paper are new and they complement previously known results.     

Almost periodic solutions for quaternion-valued shunting inhibitory cellular neural networks of neutral type with time delays in the leakage term

In this paper, we propose a class of quaternion-valued shunting inhibitory cellular neural networks of neutral type with time delays in the leakage term. In order to overcome the difficulty of the non-commutativity of quaternion multiplication, we first decompose the system under consideration into four real-valued systems. Then by using the exponential dichotomy theory of linear differential equations and Banach's fixed point theorem, we establish sufficient conditions to ensure the existence and global exponential stability of almost periodic solutions for this class of neural networks. Finally, a numerical example is given to demonstrate the effectiveness of the obtained result.     

Pseudo almost periodic solutions of discrete-time neutral-type neural networks with delays

This paper is concerned with discrete-time neutral-type neural networks with delays. The existence and uniqueness results of pseudo almost periodic solutions are established by applying the contraction mapping principal. By using some mathematical analysis techniques, we further obtain the boundness, exponential attractivity and global exponential stability of pseudo almost periodic solutions for the considered networks. Finally, a typical example and the corresponding numerical simulations have been carried out to support our analytic findings.     

Existence and global exponential stability of almost periodic solution for cellular neural networks with variable coefficients and time-varying delays

In this paper, we study cellular neural networks with almost periodic variable coefficients and time-varying delays. By using the existence theorem of almost periodic solution for general functional differential equations, introducing many real parameters and applying the Lyapunov functional method and the technique of Young inequality, we obtain some sufficient conditions to ensure the existence, uniqueness, and global exponential stability of almost periodic solution. The results obtained in this paper are new, useful, and extend and improve the existing ones in previous literature.     

New results on almost periodic solutions for CNNs with time-varying leakage delays

In this paper, based on the exponential dichotomy theory and contraction mapping fixed point theorem, we obtain some sufficient conditions ensuring the global exponential stability of almost periodic solutions for a new generalized cellular neural network model with time-varying delays in leakage (or forgetting) terms. Our results complement some recent ones. Moreover, an illustrative example and its numerical simulation are given to demonstrate the effectiveness of the obtained results.     

Dissipativity and periodic attractor for non-autonomous neural networks with time-varying delays

In this paper, a model is considered to describe the dynamics of a class of non-autonomous neural networks with time-varying delays. By applying the properties of M-matrix, the techniques of inequality analysis and the Banach fixed point theorem, we obtain a series of new criteria on the dissipativity and existence of periodic attractor. Our results can extend and improve earlier ones.     

Global exponential convergence of periodic neural networks with time-varying delays

In this paper, the global exponential convergence of a general class of periodic neural networks with time-varying delays is investigated. Based on the theory of mixed monotone operator, a testable algebraic criteria for ascertaining global exponential convergence is derived. Furthermore, the rate of exponential convergence and bound of the networks are also estimated. Finally, a numerical example is given to show the effectiveness of the obtained results.     

The almost periodic solution of Lotka-Volterra recurrent neural networks with delays

By the fixed-point theorem subject to different polyhedrons and some inequalities (e.g., the inequality resulted from quadratic programming), we obtain three theorems for the Lotka-Volterra recurrent neural networks having almost periodic coefficients and delays. One of the three theorems can only ensure the existence of an almost periodic solution, whose existence and uniqueness the other two theorems are about. By using Lyapunov function, the sufficient condition guaranteeing the global stability of the solution is presented. Furthermore, two numerical examples are employed to illustrate the feasibility and validity of the obtained criteria. Compared with known results, the networks model is novel, and the results are extended and improved.     

Almost periodic cellular neural networks with neutral-type proportional delays

This paper presents a new result on the existence, uniqueness and generalised exponential stability of almost periodic solutions for cellular neural networks with neutral-type proportional delays and D operator. Based on some novel differential inequality techniques, a testable condition is derived to ensure that all the state trajectories of the system converge to an almost periodic solution with a positive exponential convergence rate. The effectiveness of the obtained result is illustrated by a numerical example.     

Anti-periodic oscillations in fuzzy cellular neural networks with time-varying delays

This article mainly studies delayed fuzzy cellular neural networks. A sufficient criterion to guarantee the existence and exponential stability of anti-periodic solutions for this system is given. An example is given to support the obtained theoretical analysis. The obtained results play an important role in designing the neural networks and complement the earlier publications.     

On global exponential stability for impulsive cellular neural networks with time-varying delays

In this paper, the problem of global exponential stability for cellular neural networks (CNNs) with time-varying delays and fixed moments of impulsive effect is studied. A new sufficient condition has been presented ensuring the global exponential stability of the equilibrium points by using piecewise continuous Lyapunov functions and the Razumikhin technique combined with Young’s inequality. The results established here extend those given previously in the literature. Compared with the method of Lyapunov functionals as in most previous studies, our method is simpler and more effective for stability analysis.     

Multiple almost periodic solutions in nonautonomous delayed neural networks

A general methodology that involves geometric configuration of the network structure for studying multistability and multiperiodicity is developed. We consider a general class of nonautonomous neural networks with delays and various activation functions. A geometrical formulation that leads to a decomposition of the phase space into invariant regions is employed. We further derive criteria under which the n-neuron network admits 2n exponentially stable sets. In addition, we establish the existence of 2n exponentially stable almost periodic solutions for the system, when the connection strengths, time lags, and external bias are almost periodic functions of time, through applying the contraction mapping principle. Finally, three numerical simulations are presented to illustrate our theory.     

Effect of leakage delay on the almost periodic solutions of fuzzy cellular neural networks

ABSTRACT

In this paper, fuzzy cellular neural networks with time-varying delays in leakage terms are investigated. With the help of the differential inequality theory and almost periodic function theory, a set of sufficient criteria that guarantee the existence and exponential stability of almost periodic solutions of fuzzy cellular neural networks with time-varying delays in leakage terms are established. Our results are new and complement some previously known ones. Moreover, numerical simulations are carried out to verify our theoretical results.     

A shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type

In this paper, a shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type is considered. Some sufficient conditions are established to ensure that all solutions of the networks converge exponentially to zero point, which are new and complement of previously known results.     

Stability analysis of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays.

This correspondence investigates the global exponential stability problem of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays (TSFDCNNs). Based on the Lyapunov-Krasovskii functional theory and linear matrix inequality technique, a less conservative delay-dependent stability criterion is derived to guarantee the exponential stability of TSFDCNNs. By constructing a Lyapunov-Krasovskii functional, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is released in the proposed delay-dependent stability criterion. Two illustrative examples are provided to verify the effectiveness of the proposed 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．     

Existence and global exponential stability of periodic solutions of recurrent cellular neural networks with impulses and delays

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence, uniqueness and global exponential stability of periodic solutions for recurrent neural networks with impulsive perturbations and delays. Further, by using numerical simulation method, the influences of the impulsive perturbations on the inherent oscillations are investigated.