動(dòng)態(tài)分布參數(shù)神經(jīng)網(wǎng)絡(luò)時(shí)空穩(wěn)定性分析
SPATIO-TEMPORAL STABILITY ANALYSIS FOR DYNAMIC DISTRIBNTED PARAMETER NEURAL NETWORKS
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摘要: 本文將Hopfield自聯(lián)想神經(jīng)網(wǎng)絡(luò)和Kosko異聯(lián)想神經(jīng)網(wǎng)絡(luò)推廣到無窮維狀態(tài)空間動(dòng)態(tài)神經(jīng)網(wǎng)絡(luò),即動(dòng)態(tài)分布參數(shù)神經(jīng)網(wǎng)絡(luò),并給出了它們的有界性和穩(wěn)定性。尤其是還研究了帶微分算子的多維分布參數(shù)神經(jīng)網(wǎng)絡(luò)的時(shí)空穩(wěn)定性以及保證穩(wěn)定情況下所應(yīng)滿足的邊界條件。最后,還給出了一個(gè)應(yīng)用實(shí)例。Abstract: This paper extends the Hopfield s autoassociative neural networks and the Kosko s bidirectional neural networks to the dynamic neural networks with infinite state, namely the distributed parameter neural networks. Their boundedness and stability theorems are given and proved. Especially, their spatio-temporal stability is studied and their stability criteria about the boundary conditions are given. Finally, a simulation is given.
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Hopfield J J, Tank D W. Science, 1986, 233(8): 625-633.[2]Kosko B. Bidrectional associative memories. IEEE Trans. on SMC 1988, SMC-18(1): 49-60.[3]焦李成著.神經(jīng)網(wǎng)絡(luò)系統(tǒng)理論.西安:西安電子科技大學(xué)出版社,1990, 12,52-79.[4]馮大政,焦李成,保錚.動(dòng)態(tài)分布參數(shù)神經(jīng)網(wǎng)絡(luò)及其穩(wěn)定性分析. 1994年中國(guó)神經(jīng)網(wǎng)絡(luò)大會(huì)論文集.武漢:1-4.[5][5][6]廖曉昕著.穩(wěn)定性的數(shù)學(xué)理論及應(yīng)用.武漢:華中師范大學(xué)出版社,1988, 7, 79-83. -
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