ESTIMATION OF ATTRACTION DOMAIN AND EXPONENTIAL CONVERGENCE RATE OF CONTINUOUS FEEDBACK ASSOCIATIVE MEMORY

Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (3): 320-325.

ESTIMATION OF ATTRACTION DOMAIN AND EXPONENTIAL CONVERGENCE RATE OF CONTINUOUS FEEDBACK ASSOCIATIVE MEMORY

周冬明¹, 曹进德², 李继彬³

1. Department of Information and Electronic Science, Yunnan University, Kunming 650091, P. R. China;
2. Adult Education College, Yunnan University, Kunming 650091, P. R. China;
3. Center for Nonlinear Science Studies, Kunming University of Science and Technology, Kunming 650093, P. R. China

收稿日期:1999-11-01 修回日期:2000-11-19 出版日期:2001-03-18 发布日期:2001-03-18
基金资助:
the Natural Science Foundation of Yunnan Province, China(1999F0017M)

ESTIMATION OF ATTRACTION DOMAIN AND EXPONENTIAL CONVERGENCE RATE OF CONTINUOUS FEEDBACK ASSOCIATIVE MEMORY

ZHOU Dong-ming¹, CAO Jin-de², LI Ji-bin³

1. Department of Information and Electronic Science, Yunnan University, Kunming 650091, P. R. China;
2. Adult Education College, Yunnan University, Kunming 650091, P. R. China;
3. Center for Nonlinear Science Studies, Kunming University of Science and Technology, Kunming 650093, P. R. China

Received:1999-11-01 Revised:2000-11-19 Online:2001-03-18 Published:2001-03-18
Supported by:
the Natural Science Foundation of Yunnan Province, China(1999F0017M)

摘要/Abstract

摘要： The attraction domain of memory patterns and exponential convergence rate of the network trajectories to memory patterns for continuous feedback associative memory are estimated again by using of some analysis techniques and Liapunov method, some new results are obtained, that can be used for evaluation of fault-tolerance capability and the synthesis procedures for continuous feedback associative memory neural networks.

关键词: continuous feedback associative memory, Liapunov method, neural network, attraction domain, exponential convergence rate

Abstract: The attraction domain of memory patterns and exponential convergence rate of the network trajectories to memory patterns for continuous feedback associative memory are estimated again by using of some analysis techniques and Liapunov method, some new results are obtained, that can be used for evaluation of fault-tolerance capability and the synthesis procedures for continuous feedback associative memory neural networks.

Key words: continuous feedback associative memory, Liapunov method, neural network, attraction domain, exponential convergence rate

中图分类号:

O175
TP183

周冬明;曹进德;李继彬. ESTIMATION OF ATTRACTION DOMAIN AND EXPONENTIAL CONVERGENCE RATE OF CONTINUOUS FEEDBACK ASSOCIATIVE MEMORY[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(3): 320-325.

ZHOU Dong-ming;CAO Jin-de;LI Ji-bin. ESTIMATION OF ATTRACTION DOMAIN AND EXPONENTIAL CONVERGENCE RATE OF CONTINUOUS FEEDBACK ASSOCIATIVE MEMORY[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(3): 320-325.

参考文献

[1] Hopfield J J. Neurons with graded response have collective computational properties like those of two state neurons[J]. Proc Natl Acad Sci U S A, 1984,81(5):3088-3092.
[2] Michel A N, Farrel J A. Associative memories via artificial neural networks[J]. IEEE Contr Syst Mag, 1990,10(4):6-17.
[3] Guez A, Protopopolsecu V, Barhen J. On the stability, storage, capacity, and design of nonlinear continuous neural neworks[J]. IEEE Trans, 1988, SMC-18(1):80-87.
[4] Li J H, Michel A N, Porod W. Qualitative analysis and synthesis of a class of neural networks[J].IEEE Trans, 1988, CAS-35(8):976-986.
[5] Michel A N, Farrell J A, Porod W. Qualitative theory of neural networks[J]. IEEE Trnas,1989,CAS-36 (2): 229-243.
[6] Farrell J A, Michel A N. A synthesis procedure for Hopfield' s continuous-time associative memory[J]. IEEE Trans ,1990,CAS-37(7):877-884.
[7] Atiya M, Abu-Mostafu Y S. An analog feedback associative memory[J]. IEEE Trars, 1993, NN 4(1):117-126.
[8] Michel A N, Miller R K. Qualitative Analysis of Large-Scale Dynamical Systems[M]. New York:Academic, 1997,15-57.
[9] LIANG Xue-bin, WU Li-de. Estimation of attraction domain and exponential convergence rate of continuous feedback associative memory and its applications[J]. Journal of Electronics, 1996,18(1): 1-6. (in Chinese)
[10] LIANG Xue-bin, Wu Li-de. Estimation of domain of attraction and exponential convergence rate of Hopfield's continuous-tine associative memory and its applications[J]. Acta Electronica Sinica,1996,24(1):40-43. (in Chinese)
[11] CAO Jin-de. Study on attraction domain and convergence rate of Hopfield associative memory[J].Journal of Electronics, 1999,21(3): 332-336. (in Chinese)
[12] CAO Jin-de. Estimation of attraction domain and convergence rate of Hopfield associative memory and its applications[J]. Information and Control, 1999,28(7):488-491. (in Chinese)

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ESTIMATION OF ATTRACTION DOMAIN AND EXPONENTIAL CONVERGENCE RATE OF CONTINUOUS FEEDBACK ASSOCIATIVE MEMORY

ESTIMATION OF ATTRACTION DOMAIN AND EXPONENTIAL CONVERGENCE RATE OF CONTINUOUS FEEDBACK ASSOCIATIVE MEMORY

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