具有时滞的双向联想记忆神经网络的指数稳定性和周期解的存在性

通过构造Lyapunov泛函和运用不等式分析技巧，得到了判断一类时滞双向联想记忆神经网络平衡点的指数稳定性和周期解的存在性的充分条件，为综合设计具有时滞的双向联想记忆神经网络提供了依据。     

Global exponential convergence in a delayed almost periodic Nicholson's blowflies model with discontinuous harvesting

This paper is concerned with a delayed Nicholson's blowflies model with discontinuous harvesting, which is described by an almost periodic nonsmooth dynamical system. Under some reasonable assumptions on the discontinuous harvesting function, by using the Filippov regulation techniques and the theory of dichotomy, together with the Halanay inequality, we establish some new criteria on the existence of positive almost periodic solution and its convergence. An example with numerical simulation is also presented to support the theoretical results.     

Pseudo almost periodic solutions for a model of hematopoiesis with an oscillating circulation loss rate

In this paper, a model of hematopoiesis with an oscillating circulation loss rate is investigated. By applying the exponential dichotomy theory, contraction mapping fixed‐point theorem, and differential inequality techniques, a set of sufficient conditions are obtained for the existence and exponential stability of positive pseudo almost periodic solutions of the model. Some numerical simulations are carried out to support the theoretical findings. Our results improve and generalize those of the previous studies. Copyright © 2015 John Wiley & Sons, Ltd.     

Existence and exponential stability of almost‐periodic solutions for neutral BAM neural networks with time‐varying delays in leakage terms on time scales

This paper is concerned with neutral bidirectional associative memory neural networks with time‐varying delays in leakage terms on time scales. Some sufficient conditions on the existence, uniqueness, and global exponential stability of almost‐periodic solutions are established. An example is presented to illustrate the feasibility and effectiveness of the obtained results. Copyright © 2015 John Wiley & Sons, Ltd.     

Global exponential stability for the Mackey–Glass model of respiratory dynamics with a control term

This paper is concerned with the stability of positive periodic solutions for the Mackey–Glass model of respiratory dynamics with a control term. We prove the existence, positivity, and permanence of solutions, which help to deduce the global exponential stability of positive periodic solutions for this model. Our method relies upon a differential inequality technique and a Lyapunov functional. At the end, we give an example with numerical simulations to demonstrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

This paper is concerned with a class of neutral‐type BAM neural networks with distributed leakage delays. By applying the exponential dichotomy of linear differential equations, Lyapunov functional method and contraction mapping principle, we establish some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such BAM neural networks. An example is given to illustrate the effectiveness of the theoretical findings. The results obtained in this article are completely new and complement the previously known studies. Copyright © 2016 John Wiley & Sons, Ltd.     

Periodic solutions of a Lotka–Volterra type multi‐species population model with time delays

A delayed periodic Lotka–Volterra type population model with m predators and n preys is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of the model. Numerical simulation is presented to illustrate the feasibility of our main results. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

时滞分流抑制型细胞神经网络的周期解的指数稳定性

利用适当的李亚普若夫泛函,研究了时滞分流抑制型细胞神经网络的周期解的指数稳定性.     

Global exponential stability of fractional‐order impulsive neural network with time‐varying and distributed delay

In this article, we present several results on global exponential stability of a fractional‐order cellular neural network with impulses and with time‐varying and distributed delay. By using the Lyapunov‐like function methods in conjunction with the Razumikhin techniques, we derive sufficient condition for the exponential stability with an exponential convergence rate. The obtained outcomes of our present investigation significantly extend and generalize the corresponding results existing in the current literature. Finally, we give 2 illustrative examples to demonstrate the theoretical findings.     

Existence and global exponential stability of almost periodic solution for quaternion-valued high-order Hopfield neural networks with delays via a direct method

This paper deals with the existence and global exponential stability of almost periodic solutions for quaternion-valued high-order Hopfield neural networks with delays by a direct approach. Based on the contraction mapping principle, sufficient conditions are derived to ensure the existence and uniqueness of almost periodic solutions for the networks under consideration. By constructing a suitable Lyapunov function, the global exponential stability criterion of the almost periodic solution are derived. Finally, two numerical examples are given to illustrate the main results of this paper.     

Existence and global exponential stability of almost periodic solution for delayed competitive neural networks with discontinuous activations

In this paper, we study a class of delayed competitive neural networks with discontinuous activations. Without assuming the boundedness and local Lipschizian on the activation functions, some new criteria ensuring the existence and global exponential stability of almost periodic solutions for the neural network model considered in this work are established by constructing some suitable Lyapunov functionals and employing the theory of nonsmooth analysis. Finally, we present some applications and numerical examples with simulations to show the effectiveness of our main results. Copyright © 2016 John Wiley & Sons, Ltd.     

Global exponential stability for shunting inhibitory CNNs with delays

In this paper, the global exponential stability for shunting inhibitory cellular neural networks (SICNNs) with delays is studied by constructing suitable Lyapunov functionals and applying some critical analysis techniques. The sufficient conditions guaranteeing the network’s global exponential stability are obtained. Our results impose less restrictive conditions than those in the references. Moreover an example is given to illustrate the feasibility of the conditions in our results.     

Positive almost periodic solutions for a single population model with hereditary effect and mixed delays

In this paper, by using differential inequality technique, some sufficient conditions are obtained for checking the existence and global exponential stability of positive almost periodic solutions of a single population model with hereditary effect and mixed delays. Moreover, an example and its numerical simulation are given to show the effectiveness of the proposed method and results. Copyright © 2015 John Wiley & Sons, Ltd.     

Global stability of a periodic Holling‐Tanner predator‐prey model

This paper is concerned with the global dynamics of a Holling‐Tanner predator‐prey model with periodic coefficients. We establish sufficient conditions for the existence of a positive solution and its global asymptotic stability. The stability conditions are first given in average form and afterward as pointwise estimates. In the autonomous case, the previous criteria lead to a known result.     

On contraction of nonlinear difference equations with time‐varying delays

General nonlinear difference equations with time‐varying delays are considered. Explicit criteria for contraction of such equations are presented. Then some simple sufficient conditions for global exponential stability of equilibria and for stability of invariant sets are derived. Furthermore, explicit criteria for existence, uniqueness and global exponential stability of periodic solutions are derived. Finally, the obtained results are applied to time‐varying discrete‐time neural networks with delay.     

Almost periodic solutions for neutral‐type neural networks with the delays in the leakage term on time scales

In this paper, a class of neutral‐type neural networks with delays in the leakage term on time scales are considered. By using the Banach fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solutions for this class of neural networks. The results of this paper are new and complementary to the previously known results. Finally, an example is presented to illustrate the effectiveness of our results. Copyright © 2016 John Wiley & Sons, Ltd.     

Existence and exponential stability of almost periodic solutions for a neutral multi-species Logarithmic population model

In this paper, we study the almost periodic solution for a neutral multi-species Logarithmic population model. By employing Banach’s fixed point theorem and using differential inequality technique, we present some sufficient conditions ensuring the existence, uniqueness and globally exponential stability of almost periodic solution for the model. The results obtained extend and improve the earlier publications. Finally, two examples are provided to show the correctness of our analysis.     

Existence and global exponential stability of almost periodic solutions for BAM neural networks with distributed leakage delays on time scales

In this paper, we deal with a class of BAM neural networks with distributed leakage delays on time scales. Some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such class of BAM neural networks are obtained by applying the exponential dichotomy of linear differential equations, Lapunov functional method and contraction mapping principle. An example is given to illustrate the effectiveness of the theoretical predictions. The obtained results in this paper are completely new and complement the previously known publications.     

Global lagrange stability of complex‐valued neural networks of neutral type with time‐varying delays

In this article, the problem of global exponential stability in Lagrange sense of neutral type complex‐valued neural networks (CVNNs) with delays is investigated. Two different classes of activation functions are considered, one can be separated into real part and imaginary part, and the other cannot be separated. Based on Lyapunov theory and analytic techniques, delay‐dependent criteria are provided to ascertain the aforementioned CVNNs to be globally exponentially stable GES in Lagrange sense. Moreover, the proposed sufficient conditions are presented in the form of linear matrix inequalities which could be easily checked by Matlab. Finally, two simulation examples are given out to demonstrate the validity of theory results. © 2016 Wiley Periodicals, Inc. Complexity 21: 438–450, 2016     

具有时滞的扩散BAM神经网络的指数稳定性

研究一类具有反应扩散的滞后BAM神经网络平衡点的存在性唯一性和全局指数稳定性.运用拓扑同胚映射,Lyapunov泛函以及多参数方法,得到关于平衡点存在唯一性和全局指数稳定性的充分条件,将相关文献的结果推广到正整数r范数上.