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A critical analysis on global convergence of Hopfield-type neural networks
Peng, JG; Xu, ZB; Qiao, H; Zhang, B
Source PublicationIEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
2005-04-01
Volume52Issue:4Pages:804-814
SubtypeArticle
AbstractThis paper deals with the global convergence and stability of the Hopfield-type neural networks under the critical condition that M-1 (Gamma) = L-1 D Gamma - (Gamma W + W(T)Gamma) / (2) is nonnegative for any diagonal matrix Gamma, where W is the eight matrix of the network, L = diag {L-1, L-2,..., L-N} with L-i being the Lipschitz constant of g(i) and G(u) = (g(1)(u(1)),g(2)(u(2)),...g(N)(u(N)))(T) is the activation mapping of the network. Many stability results have been obtained for the Hopfield-type neural networks in the noncritical case that M-1 (Gamma) is positive definite -for some positive definite diagonal matrix F. However, very few results are available on the global convergence and stability of the networks in the critical case. In this paper, by exploring two intrinsic features of the activation mapping, two generic global convergence results are established in the critical case for the Hopfield-type neural networks, which extend most of the previously known globally asymptotic stability criteria to the critical case. The results obtained discriminate the critical dynamics of the networks, and can be applied directly to a group of Hopfield-type neural network models. An example has also been presented to demonstrate both theoretical importance and practical significance of the critical results obtained.
KeywordAttractive Global Convergence Hopfield-type Neural Networks Stability Analysis
WOS HeadingsScience & Technology ; Technology
WOS KeywordEXPONENTIAL STABILITY ; ASSOCIATIVE MEMORIES ; BOUND CONSTRAINTS ; DYNAMICAL-SYSTEMS ; OPTIMIZATION ; CIRCUITS
Indexed BySCI
Language英语
WOS Research AreaEngineering
WOS SubjectEngineering, Electrical & Electronic
WOS IDWOS:000228228200013
Citation statistics
Cited Times:26[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.ia.ac.cn/handle/173211/9167
Collection09年以前成果
Corresponding AuthorPeng, JG
Affiliation1.Xian Jiaotong Univ, Fac Sci, Inst Informat & Syst Sci, Xian 710049, Peoples R China
2.Chinese Acad Sci, Inst Automat, Beijing 100080, Peoples R China
3.Univ Manchester, Sch Informat, Manchester M60 1QD, Lancs, England
4.Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China
5.Coventry Univ, Sch MIS, Coventry CV1 5FB, W Midlands, England
Recommended Citation
GB/T 7714
Peng, JG,Xu, ZB,Qiao, H,et al. A critical analysis on global convergence of Hopfield-type neural networks[J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS,2005,52(4):804-814.
APA Peng, JG,Xu, ZB,Qiao, H,&Zhang, B.(2005).A critical analysis on global convergence of Hopfield-type neural networks.IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS,52(4),804-814.
MLA Peng, JG,et al."A critical analysis on global convergence of Hopfield-type neural networks".IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 52.4(2005):804-814.
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