模擬神經網絡穩(wěn)定性研究
RESEARCHES ON THE STABILITIES OF ANALOG ELECTRONIC NEURAL NETWORKS
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摘要: 本文提出了模擬神經網絡穩(wěn)定性分析的靜態(tài)等效模型,通過推廣特勒根定理,從等效模型導出了物理意義清晰的能量函數。由一階微分方程組求網絡能量函數的方法普適于所有的一階連續(xù)自治系統(tǒng)。文章并利用能量平穩(wěn)原理對點格神經網絡的穩(wěn)定性質進行了討論,得到了一些對于網絡的電路實現(xiàn)具有一定指導意義的結果。Abstract: A new method for analysing the stabilities of analog electronic neural networks is presented. The energy functions with clear and definite physical meaning are derived by introducing the static equivalent circuit models, which has expanded the Tellegen Theorem for application on circuit analysis. The method used to derive the energy functions of nets from first order differential equations is valid for all first order continuous autonomous systems. The stability analysis of cellular neural networks is made by the use of stationary cocontent theorem. Some results are instructive for the network implementation on circuits.
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J.J.Hopfield, Proc. Natl. Acad. Sci. U.S.A., 79(1982), 2554.[2]J.J.Hopfield, D.W. Tank, Science, 233(1986),625.[3]A.Desoer, S. Kuh, Basic circuit theory, McGraw-Hill, N.Y., (1969).[4]L.O. Chua, J. Frankin Inst.,296(1973)2,9.[5]L.O. Chua, Lin Yang, IEEE, Trans. on CAS, CAS-35(1988)10,1257.[6]K. Preston, Jr. M.J.B. Daff, Modern Cellular automata: theory and Application, New York, Plenum, (1984).[7]J. Hopfield, Proc. Natl. Acad. Sci. U.S.A., 81(1984), 3088. -
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