一类新的变时滞中立型神经网络的全局渐近稳定性条件

数学物理学报 ›› 2015, Vol. 35 ›› Issue (3): 634-640.

• 论文 • 上一篇

一类新的变时滞中立型神经网络的全局渐近稳定性条件

罗日才¹, 许弘雷², 王五生³

1. 河池学院计算机与信息工程学院广西宜州 546300;
2. Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia;
3. 河池学院计数学与统计学院广西宜州 546300

收稿日期:2014-04-29 修回日期:2014-10-10 出版日期:2015-06-25 发布日期:2015-06-25
作者简介:罗日才, luoricai@163.com;许弘雷, hongleix@gmail.com;王五生, wang4896@126.com
基金资助:
国家自然科学基金(11171079)和广西教育厅科研项目(201106LX591)资助

Globally Asymptotic Stability of A New Class of Neutral Neural Networks with Time-Varying Delays

Luo Ricai¹, Xu Honglei², Wang Wusheng³

1. School of Computer and Information Engineering, Hechi University, Guangxi Yizhou 546300;
2. Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia;
3. School of Mathematics and Statistics, Hechi University, Guangxi Yizhou 546300

Received:2014-04-29 Revised:2014-10-10 Online:2015-06-25 Published:2015-06-25

摘要/Abstract

摘要：

研究了一类激活函数的状态变量带有微分时滞的中立型神经网络的稳定性问题. 通过构造李亚普诺夫函数, 并利用LMI分析技巧, 获得了该类中立型神经网络的全局渐近稳定性的充分条件. 最后通过实际算例验证了所得结果的有效性.

关键词: 中立型神经网络, 变时滞, 全局渐近稳定性, 充分条件

Abstract:

In this paper, we study the stability problem of a class of neural neutral network systems whose involve an activation function with differential time-delay state variables. By constructing Lyapunov functions and using LMI techniques, we obtain a sufficient condition for the global asymptotic stability of these neural networks. Finally, we demonstrate the validity of our results by use of a numerical example.

Key words: Neutral neural networks, Varying time delays, Global asymptotic stability, Sufficient condition

中图分类号:

O175

罗日才, 许弘雷, 王五生. 一类新的变时滞中立型神经网络的全局渐近稳定性条件[J]. 数学物理学报, 2015, 35(3): 634-640.

Luo Ricai, Xu Honglei, Wang Wusheng. Globally Asymptotic Stability of A New Class of Neutral Neural Networks with Time-Varying Delays[J]. Acta mathematica scientia,Series A, 2015, 35(3): 634-640.

参考文献

[1] Hopfield J J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc Aead Sci USA, 1984, 81: 3088-3092
[2] Abe S, Kawakami J, Hirasawa K. Solving inequality constrained combinatorial optimization problems by the hopfield neural networks. Neural Networks, 1992, 5: 663-670
[3] Tamura H, Zhang Z, Xu X S, Ishii M, Tang Z. Lagrangian object relaxation neural network for combinatorial optimization problems. Neurocomputing, 2005, 68: 297-305
[4] Wang R L, Tang Z, Cao Q P. A learning method in Hopfield neural network for combinatorial optimization problem. Neurocomputing, 2002, 48: 1021-1024
[5] Rout S, Seethalakshmy, Srivastava P, Majumdar J. Multi-modal image segmentation using a modified Hopfield neural network. Pattern Recognition, 1998, 31: 743-750
[6] Sammouda R, Adgaba N, Touir A, Al-Ghamdi A. Agriculture satellite image segmentation using a modified artificial Hopfield neural network. Computers in Human Behavior, 2014, 30: 436-441
[7] Suganthan P, Teoh E, Mital D. Pattern recognition by homomorphic graph matching using Hopfield neural networks. Image and Vision Computing, 1995, 13: 45-60
[8] Laskaris N, Fotopoulos S, Papathanasopoulos P, Bezerianos A. Robust moving averages, with Hopfield neural network implementation, for monitoring evoked potential signals. Electroencephalography and Clinical Neurophysiology/Evoked Potentials Section, 1997, 104: 151-156
[9] Calabuig D, Monserrat J F, Gmez-Barquero D, Lzaro O. An efficient dynamic resource allocation algorithm for packet-switched communication networks based on Hopfield neural excitation method. Neurocomputing, 2008, 71: 3439-3446
[10] Zhang W. A weak condition of globally asymptotic stability for neural networks. Applied Mathematics Letters, 2006, 19: 1210-1215
[11] Li X. Zhang Chen. Stability properties for Hopfield neural networks with delays and impulsive perturbations. Nonlinear Analysis: Real World Applications, 2009, 10: 3253-3265
[12] Wang L. Yuying Gao. Global exponential robust stability of reaction-diffusion interval neural networks with time-varying delays. Physics Letters A, 2006, 350: 342-348
[13] Lou X, Ye Q, Cui B. Parameter-dependent robust stability of uncertain neural networks with time-varying delay. Journal of the Franklin Institute, 2012, 349: 1891-1903
[14] Bai C. Global stability of almost periodic solutions of Hopfield neural networks with neutral time-varying delays. Applied Mathematics and Computation, 2008, 203: 72-79
[15] Marcus C, Westervelt R. Stability of analog neural networks with delay. Phys Rev, 1989, 39A: 347-359
[16] Wu J. Symmetric functional-differential equations and neural networks with memory. Trans Am Math Soc, 1999, 350: 4799-4838
[17] Wu J, Zou X. Patterns of sustained oscillations in neural networks with time delayed interactions. Appl Math Comput, 1995, 73: 55-75
[18] Gopalsamy K, He X. Stability in asymmetric Hopfield nets with transmission delays. Physica D, 1994, 76: 1344-358
[19] van den Driessche P, Zou X. Global attractivity in delayed Hopfield neural network models. SIAM J Appl Math, 1998, 58: 1878-1890
[20] Orman Z. New sufficient conditions for global stability of neutral-type neural networks with time delays. Neurocomputing, 2012, 97: 141-148
[21] Zhao H. Global asymptotic stability of Hopfield neural network involving distributed delays. Neural Networks, 2004, 17: 47-53
[22] Rakkiyappan R, Balasubramaniam P. Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays. Applied Mathematics and Computation, 2008, 198: 526-533
[23] Xu H, Chen Y, Teo K L. Global exponential stability of impulsive discrete-time neural networks with time-varying delays. Applied Mathematics and Computations, 2010, 217: 537-544
[24] Chen Y, Xu H. Exponential stability analysis and impulsive tracking control of uncertain time-delayed systems. Journal of Global Optimization, 2012, 52: 323-334
[25] 陈武华, 卢小梅, 李群宏等. 随机Hopfield时滞神经网络均方指数稳定性: LMI方法. 数学物理学报, 2007, 27(1): 109-117

一类新的变时滞中立型神经网络的全局渐近稳定性条件

Globally Asymptotic Stability of A New Class of Neutral Neural Networks with Time-Varying Delays

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 12

Metrics

本文评价

推荐阅读 0

[1]	李棒, 余旌胡. 基于Schur-凸的不完全信息下的不平等性比较[J]. 数学物理学报, 2018, 38(2): 334-349.
[2]	杨甲山, 李同兴. 时间模上一类二阶阻尼Emden-Fowler型动态方程的振荡性[J]. 数学物理学报, 2018, 38(1): 134-155.
[3]	黄祖达. 一类具反馈控制的时滞飞蝇方程的伪概周期解[J]. 数学物理学报, 2016, 36(3): 558-568.
[4]	阿卜杜杰力力·阿卜杜热合曼, 蒋海军, 滕志东. 具有混合变时滞的脉冲Cohen-Grossberg神经网络的指数同步[J]. 数学物理学报, 2015, 35(3): 545-557.
[5]	李俊民. 非线性参数化时变时滞系统自适应迭代学习控制[J]. 数学物理学报, 2011, 31(3): 682-690.
[6]	吴事良, 刘三阳. 反应扩散系统双稳波前解的全局渐近稳定性[J]. 数学物理学报, 2010, 30(2): 440-448.
[7]	王根强; 燕居让. 多变时滞 n 阶非线性中立型泛函微分方程周期解存在性[J]. 数学物理学报, 2006, 26(2): 306-313.
[8]	彭建文;朱道立. 严格 B -预不变凸函数[J]. 数学物理学报, 2006, 26(2): 200-206.
[9]	曾志刚, 廖晓昕. 无界变时滞神经网络全局稳定性[J]. 数学物理学报, 2005, 25(5): 621-626.
[10]	王根强, 燕居让. 多变量时滞n阶非线性非自治微分方程周期解存在性[J]. 数学物理学报, 2003, 23(4): 431-435.
[11]	滕志东. 一类无穷时滞周期Lotka-Volterra型系统的正周期解[J]. 数学物理学报, 2001, 21(1): 94-101.
[12]	滕志东陈兰荪. 具有时滞的周期Lotka-Volterra型系统的全局渐近稳定性[J]. 数学物理学报, 2000, 20(3): 296-303.