时标上具Allee效应的动力学方程的概周期解

本文研究了时标上具Allee效应的可再生资源动力学方程的概周期解的存在性与稳定性.利用线性系统指数二分性与压缩映射不动点定理,得到了方程存在唯一概周期解的充分条件.此外,通过构建适当的Laypunov函数,得到了概周期解是全局指数稳定的充分条件.     

一类2维微分方程的概周期解

本文利用指数型二分性理论和 Liapunov 函数方法,研究了一类2维微分方程的概周期解的存在性,得到了非常简洁的充分条件.用所得到的结果,讨论了几类二阶微分方程的概周期解.得到了一些新的结果.     

时标上具Allee效应的动力学方程的概周期解（英文）

本文研究了时标上具Allee效应的可再生资源动力学方程的概周期解的存在性与稳定性.利用线性系统指数二分性与压缩映射不动点定理,得到了方程存在唯一概周期解的充分条件.此外,通过构建适当的Laypunov函数,得到了概周期解是全局指数稳定的充分条件.     

二次概周期系数微分方程的概周期解

利用指数二分性,Schauder不动点定理和Grownwall不等式证明了一类概周期系数微分方程的概周期解、有界解的存在唯一性及概周期解的全局吸引性.     

Ezeilo概周期解存在的性定理的推广

本文利用指数型二分性理论讨论了一般高维概周期系统的概周期解的存在性和唯一性,所得结果推广了Ｅｚｅｉｌｏ的一个概周期解的存在性定理。     

弱概周期微分方程的弱概周期解

本文利用微分方程的指数型三分性给出了弱概周期微分方程的弱概周期解的存在性定理,并讨论了弱概周期微分方程的一些性质,从而改进了文献[2—7]中的一些结果.     

Ezeilo概周期解存在性定理的推广

本文利用指数型二分性理论讨论了一般高维概周期系统的概周期解的存在性和唯一性，所得结果推广了Ｅｚｅｉｌｏ的一个概周期解的存在性定理     

具S-型分布时滞的细胞神经网络的概周期解

该文研究一类具S-型分布时滞的细胞神经网络(CNNs)的概周期解及全局指数型稳定性问题.利用指数型二分性和Schauder不动点定理以及构造Lyapunov函数,得到了细胞神经网络模型概周期解和指数稳定性的一些充分条件.此外,给出一个实例说明结果是可行的.     

时延细胞神经网络的概周期解的存在性和指数稳定性

研究时延细胞神经网络的概周期解存在性和全局指数稳定性问题 ,巧妙地引入可调实参数di>0 (i =1,2 ,… ,n) ,获得了该神经网络存在唯一的概周期解的充分条件和所有其它解均指数地收敛于此概周期解的充分条件 .     

具无穷时滞的中立型Volterra积分微分方程的概周期解

研究了一类具无穷时滞的中立型Volterra积分微分方程的概周期解问题．利用线性系统指数型二分性理论和泛函分析方法,得到了一些关于该方程的概周期解的存在性、唯一性与稳定性的新结果,推广了相关文献的主要结果．     

Weighted pseudo almost periodic solutions of neutral functional differential equations

In this paper, we study weighted pseudo almost periodic solutions of neutral functional differential equations. By applying the properties of weighted pseudo almost periodic functions and the exponential dichotomy of linear systems as well as Krasnoselskii’s fixed point theorem, we establish the conditions for the existence of weighted pseudo-almost periodic solution of the equations.     

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 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.     

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.     

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 stability of almost periodic solutions of Hopfield neural networks with continuously distributed delays

In this paper, the global stability and almost periodicity are investigated for Hopfield neural networks with continuously distributed neutral delays. Some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper are new and they complement the previously known ones. Finally, an example is given to demonstrate the effectiveness of our results.     

时滞细胞神经网络概周期解的存在性与全局指数稳定性

通过利用Banach 空间中的不动点定理和Lyapunov泛函的方法,获得了时滞细胞神经网络概周期解的存在性与全局指数稳定性的新结论. 所获结果在较大程度上改进和推广了已有文献中的相应结果.     

Positive almost periodic solutions for recurrent neural networks

In this paper recurrent neural networks with time-varying delays and continuously distributed delays are considered. Sufficient conditions for the existence and exponential stability of the positive almost periodic solutions are established, which are new and complement previously known results.     

Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses

In this paper, by using the contraction principle and Gronwall–Bellman’s inequality, some sufficient conditions are obtained for checking the existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks (SICNNs) with impulse. Our results are essentially new. It is the first time that the existence of almost periodic solutions for the impulsive neural networks are obtained.