Impulsive Control for Existence, Uniqueness, and Global Stability of Periodic Solutions of Recurrent Neural Networks With Discrete and Continuously Distributed Delays

Li X.; Song S.

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Impulsive Control for Existence, Uniqueness, and Global Stability of Periodic Solutions of Recurrent Neural Networks With Discrete and Continuously Distributed Delays

机译：具有离散和连续分布时滞的递归神经网络周期解的存在性，唯一性和全局稳定性的脉冲控制

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摘要

In this paper, a class of recurrent neural networks with discrete and continuously distributed delays is considered. Sufficient conditions for the existence, uniqueness, and global exponential stability of a periodic solution are obtained by using contraction mapping theorem and stability theory on impulsive functional differential equations. The proposed method, which differs from the existing results in the literature, shows that network models may admit a periodic solution which is globally exponentially stable via proper impulsive control strategies even if it is originally unstable or divergent. Two numerical examples and their computer simulations are offered to show the effectiveness of our new results.

机译：在本文中，考虑了一类具有离散且连续分布的延迟的递归神经网络。利用压缩映射定理和脉冲泛函微分方程的稳定性理论，获得了周期解的存在性，唯一性和全局指数稳定性的充分条件。所提出的方法与文献中已有的结果不同，它表明网络模型可以接受一个周期解，该周期解通过适当的脉冲控制策略在全局上是指数稳定的，即使它最初是不稳定的或发散的。提供了两个数值示例及其计算机模拟，以证明我们新结果的有效性。

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《Neural Networks and Learning Systems, IEEE Transactions on》 |2013年第6期|868-877|共10页
作者
Li X.; Song S.;
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作者单位

School of Mathematical Sciences, Shandong Normal University, Ji''nan, China;

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正文语种 eng
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关键词
Contraction mapping theorem; delays; existence; impulsive control; periodic solution; recurrent neural networks; stability theory; uniqueness;

机译：收缩映射定理;延误存在;冲动控制周期解递归神经网络稳定性理论;独特性;

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专利

1. Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays [J] . Li XD Applied mathematics and computation . 2009,第1期

机译：具有连续分布时滞的脉冲Cohen-Grossberg型BAM神经网络周期解的存在性和全局指数稳定性
2. EXISTENCE AND EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS TO BAM RECURRENT NEURAL NETWORKS WITH TRANSMISSION DELAYS AND CONTINUOUSLY DISTRIBUTED DELAYS [J] . 微分方程年刊：英文版 . 2012,第004期

机译：具有传输延迟和连续分布延迟的BAM递归神经网络的概周期解的存在性和指数稳定性。
3. Existence and global exponential stability of periodic solution to BAM neural networks with periodic coefficients and continuously distributed delays [J] . Zhou TJ, Chen AP, Zhou YY Physics Letters, A . 2005,第5期

机译：具有周期系数和连续分布时滞的BAM神经网络周期解的存在性和全局指数稳定性
4. Global Exponential Stability and Existence of Periodic Solution of Hopfield-type Neural Networks with Distributed Delays and Impulsive On Time Scales [C] . Chaolong Zhang, Qiru Wang, Fengjian Yang, World Congress on Intelligent Control and Automation;WCICA 2010 . 2010

机译：具有时滞和脉冲时滞的Hopfield型神经网络的全局指数稳定性和周期解的存在性
5. Optimization problems arising in stability analysis of discrete time recurrent neural networks. [D] . Singh, Jayant. 2016

机译：离散时间递归神经网络稳定性分析中出现的优化问题。
6. Global Exponential Stability of Almost Periodic Solution for Neutral-Type Cohen-Grossberg Shunting Inhibitory Cellular Neural Networks with Distributed Delays and Impulses [O] . Lijun Xu, Qi Jiang, Guodong Gu 2016

机译：具有分布时滞和脉冲的中立型Cohen-Grossberg分流抑制性细胞神经网络的概周期解的全局指数稳定性
7. EXISTENCE AND EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR CELLULAR NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS [O] . Bingwen Liu, Lihong Huang 2006

机译：几乎具有连续分布延迟的蜂窝神经网络几乎定期解决方案的存在和指数稳定性

Impulsive Control for Existence, Uniqueness, and Global Stability of Periodic Solutions of Recurrent Neural Networks With Discrete and Continuously Distributed Delays

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