[1]宿 娟.时滞Hopfield神经网络全局渐近稳定的弱条件[J].四川师范大学学报(自然科学版),2018,(03):381-386.[doi:10.3969/j.issn.1001-8395.2018.03.018]
 SU Juan.A Weak Condition of Globally Asymptotic Stability for Hopfield Neural Networks with Time Delays[J].Journal of SichuanNormal University,2018,(03):381-386.[doi:10.3969/j.issn.1001-8395.2018.03.018]
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时滞Hopfield神经网络全局渐近稳定的弱条件()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年03期
页码:
381-386
栏目:
基础理论
出版日期:
2018-03-15

文章信息/Info

Title:
A Weak Condition of Globally Asymptotic Stability for Hopfield Neural Networks with Time Delays
文章编号:
1001-8395(2018)03-0381-06
作者:
宿 娟
成都师范学院 数学学院, 四川 成都 610044
Author(s):
SU Juan
Department of Mathematics, Chengdu Normal College, Chengdu 610044, Sichuan
关键词:
Hopfield神经网络 时滞 全局渐近稳定 弱条件
Keywords:
Hopfield neural networks time delays globally asymptotic stability weak condition
分类号:
O29; TP183
DOI:
10.3969/j.issn.1001-8395.2018.03.018
文献标志码:
A
摘要:
研究时滞Hopfield神经网络全局渐近稳定的弱条件,其中系统的激活函数没有有界和可微的限制,比S型的要求更弱.首先构造一个Lyapunov函数,计算得到沿系统解的右上Dini导数非正,从而获得平衡点的局部稳定性.然后利用反证和分析方法,进一步证明该Lyapunov函数在时间趋于无穷时的极限为0,从而获得平衡点的全局吸引性.结合局部稳定性和全局吸引性,说明系统是全局渐近稳定的,且平衡点唯一.
Abstract:
This paper studies the weak condition of globally asymptotic stability for Hopfield neural networks with time delays. The activation functions employed in the system may not be bounded or differentiable, which are less constrained than the S type. Firstly, by constructing a Lyapunov function, I calculate its upper right Dini along the solution of the system. The non-positivity of the derivative under the restraint of parameters of the system indicates that the equilibrium of the system is locally stable. Then by the analysis method, the limit of the Lyapunov function is proved to be 0 as time approaches infinity. Thus, the global attractivity of the equilibrium is obtained. Together with the local stability and global attractivity of equilibrium, we derive a sufficient condition of globally asymptotic stability of the system, which implies the uniqueness of equilibrium.

参考文献/References:

[1] HOPFIELD J. Neurons with graded response have collective computational properties like those of two-stage neurons[J]. Proc Natl Acad Sci USA,1984,81:3088-3092.
[2] TANK D, HOPFIELD J. Simple “neural” optimization networks:an A/D converter, signal decision circuit, and a linear programming circuit[J]. IEEE Trans Circuits Syst,1986,33(5):533-541.
[3] HOPFIELD J, TANK D. Neural computation of decision optimization problems[J]. Biol Cybernet,1985,52:141-154.
[4] TALAVAN P, YANEZ J. Parameter setting of the Hopfield networks applied to TSP[J]. Neural Networks,2002,15(3):363-373.
[5] FORTI M, TESI A. New conditions for global stability of neural networks with application to linear and quadratic programming problems[J]. IEEE Trans Circuits Syst I,1995,42(7):354-365.
[6] LEE D. Pattern sequence recognition using a time-varying Hopfield networks[J]. IEEE Trans Neural Netw,2002,13(2):330-342.
[7] FARREL J, MICHEL A. A synthesis procedure for Hopfield's continuous-time associative memory[J]. IEEE Trans Circuits Syst,1990,37(7):877-884.
[8] CHENG C, LIN K, SHIH C. Multistability in recurrent neural networks[J]. SIAM J Appl Math,2006,66(4):1301-1320.
[9] HAYKIN S. Neural Networks:A Comprehensive Foundation[M]. New Jersey:Prentice-Hall,1998.
[10] MICHEL A, FARRELL J, POROOD W. Qualitative analysis of neural networks[J]. IEEE Trans Circuits and Systems,1989,36(2):229-243.
[11] WU J. Introduction to Neural Dynamics and Signal Transmission Delay[M]. Berlin:Walter de Gruyter,2001.
[12] MARCUS C, WESTERVELT R. Stability of analog neural networks with delay[J]. Phys Rev,1989,A39:347-359.
[13] GOPALSAMY K, HE X. Stability in asymmetric Hopfield nets with transmission delays[J]. Physica D,1994,76:344-358.
[14] DRIESSCHE P, ZOU X. Global attractivity in delayed Hopfield neural network models[J]. SIAM J Appl Math,1998,58(6):1878-1890.
[15] ZHANG J, JIN X. Global stability analysis in delayed Hopfield neural networks models[J]. Neural Networks,2000,13:745-753.
[16] MARCO M, FORTI M, GRANZZINI M, et al. Limit set dichotomy and multistability for a class of cooperative neural networks with delays[J]. IEEE Trans Neural Netw Learn Syst,2012,23(9):1473-1485.
[17] CHENG C, LIN K, SHIH C, et al. Multistability for delayed neural networks via sequential contracting[J]. IEEE Trans Neural Netw Learn Syst,2015,26(12):3109-3122.
[18] EDUARDO L, ALFONSO R. Attractivity, multistability,and bifurcation in delayed Hopfield's model with non-monotonic feedback[J]. J Diff Eqns,2013,255:4244-4266.
[19] CHEN T. New theorems on global convergece of some dynamical systems[J]. Neural networks,2001,14:251-255.
[20] Zhang W. A weak condition of globally asymptotic stability for neural networks[J]. Applied Mathematics Letters,2006,19:1210-1215.
[21] CHEN T, AMARI S. Stability of asymmetric Hopfield networks[J]. IEEE Trans Neural Networks,2001,12(1):159-163.
[22] ROUCHE N, HABETS P, LALOR M. Stability theory by Lyapunov's Direct Method[M]. New York:Springer-Verlag,1977.

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备注/Memo

备注/Memo:
收稿日期:2016-12-22 接受日期:2017-02-16
基金项目:四川省教育厅自然科学一般项目(18ZB0094)和四川省教育厅自然科学重点项目(15ZA0135)
作者简介:宿 娟(1980—),女,讲师,主要从事微分方程与动力系统的研究,E-mail:sujuanmath@163.com
更新日期/Last Update: 2018-03-15