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1.
In this paper, we deal with some theorems on the exponential stability of trivial solution of time-varying non-regressive dynamic equation on time scales with bounded graininess. In particular, well-known Perron's theorem is generalized on time scales. Under rather restrictive condition, that is, integral boundedness of coefficient operators, we obtain a characterization of the uniformly exponential stability. 相似文献
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Weighted pseudo‐almost periodic functions on time scales with applications to cellular neural networks with discrete delays
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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. 相似文献
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Existence and global stability of almost automorphic solutions for shunting inhibitory cellular neural networks with time-varying delays in leakage terms on time scales
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In this paper, shunting inhibitory cellular neural networks(SICNNs) with time-varying delays in leakage terms on time scales are investigated. With the aid of the existence of the exponential dichotomy of linear dynamic equations on time scales, fixed point theorem and the theory of calculus on time scales, we establish some sufficient conditions to ensure the existence and exponential stability of almost automorphic solutions for the model. An example with its numerical simulations is given to illustrate the feasibility and effectiveness of the theoretical findings. 相似文献
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Existence and global exponential stability of almost periodic solutions for BAM neural networks with distributed leakage delays on time scales
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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. 相似文献
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This paper studies scale-type stability for neural networks with unbounded time-varying delays and Lipschitz continuous activation functions. Several sufficient conditions for the global exponential stability and global asymptotic stability of such neural networks on time scales are derived. The new results can extend the existing relevant stability results in the previous literatures to cover some general neural networks. 相似文献
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Almost periodic solutions for neutral‐type neural networks with the delays in the leakage term on time scales
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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. 相似文献
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The main objective of this study is two-fold: First, we provide necessary and sufficient conditions for the positivity of Volterra integro-dynamical systems on time scales by means of Metzler matrices. Secondly, we show that positivity of the system implies uniform exponential stability of the trivial solution under sufficient conditions. 相似文献
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微分方程的指数稳定性 总被引:1,自引:0,他引:1
比较系统地研究了It方程解的指数稳定性.给出了随机指数稳定性、指数P-稳定性、几乎必然指数稳定性的比较准则,这些比较准则推广了Nevel’son和Has’minskiǐ的相应结果. 相似文献
10.
Existence and exponential stability of almost‐periodic solutions for neutral BAM neural networks with time‐varying delays in leakage terms on time scales
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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. 相似文献
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变时滞细胞神经网络的指数稳定的一个充分条件 总被引:1,自引:0,他引:1
本文我们研究了变时滞细胞神经网络的指数稳定性。利用分析技巧,获得了变时滞细胞神经网络的指数稳定的充分条件,改进了已有文献中的相应结果。 相似文献
12.
Weyl almost automorphy is a natural generalization of Bochner almost automorphy and Stepanov almost automorphy. However, the space composed of Weyl almost automorphic functions is not a Banach space. Therefore, the results of the existence of Weyl almost automorphic solutions of differential equations are few, and the results of the existence of Weyl almost automorphic solutions of difference equations are rare. Since the study of dynamic equations on time scales can unify the study of differential equations and difference equations. Therefore, in this paper, we first propose a concept of Weyl almost automorphic functions on time scales and then take the Clifford-valued shunt inhibitory cellular neural networks with time-varying delays on time scales as an example of dynamic equations on time scales to study the existence and global exponential stability of their Weyl almost automorphic solutions. We also give a numerical example to illustrate the feasibility of our results. 相似文献
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Zhang Hai~ 《Annals of Differential Equations》2007,23(4):564-569
The global exponential stability of the zero solution to a class of differential system with delay is considered.By constructing a suitable type of Lyapunov functional and using some analytical techniques,we derive some criteria to check exponential stability of this system.The results establish a relation between the delay time and the parameters of the system.Two examples are also given to illustrate the validity of the results. 相似文献
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时滞Hopfield神经网络模型的全局吸引性和全局指数稳定性 总被引:6,自引:0,他引:6
对具有时滞的Hopfield神经网络模型,在非线性神经元激励函数是Lipschitz连续(而非已有的大部分文献中假设是Sigmoid函数)的条件下,通过构造适当的泛函,给出了这类模型全局吸引和平衡点全局指数稳定的易于验证的充分条件。 相似文献
17.
Existence and exponential stability of unique almost periodic solution for Lasota–Wazewska red blood cell model with perturbation on time scales
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Zhijian Yao 《Mathematical Methods in the Applied Sciences》2017,40(13):4709-4715
This paper deals with Lasota–Wazewska red blood cell model with perturbation on time scales. By applying the fixed point theorem of decreasing operator, we establish sufficient conditions for the existence of unique almost periodic positive solution. Particularly, we give iterative sequence which converges to the almost periodic positive solution. Moreover, we investigate exponential stability of the almost periodic positive solution by means of Gronwall inequality. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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避免构造Lyapunov函数的困难,运用广义Dahlquist数方法研究了Cohen- Grossberg神经网络模型的指数稳定性,不但得到了Cohen-Grossberg神经网络平衡点存在惟一性和指数稳定性的全新充分条件,而且给出了神经网络的指数衰减估计.与已有文献结果相比,所得的神经网络指数稳定的充分条件更为宽松,给出的解的指数衰减速度估计也更为精确. 相似文献
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Pham Huu Anh Ngoc Hieu Trinh Le Trung Hieu Nguyen Dinh Huy 《Mathematische Nachrichten》2019,292(4):859-870
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. 相似文献