动态分布参数神经网络时空稳定性分析
SPATIO-TEMPORAL STABILITY ANALYSIS FOR DYNAMIC DISTRIBNTED PARAMETER NEURAL NETWORKS
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摘要: 本文将Hopfield自联想神经网络和Kosko异联想神经网络推广到无穷维状态空间动态神经网络,即动态分布参数神经网络,并给出了它们的有界性和稳定性。尤其是还研究了带微分算子的多维分布参数神经网络的时空稳定性以及保证稳定情况下所应满足的边界条件。最后,还给出了一个应用实例。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.神经网络系统理论.西安:西安电子科技大学出版社,1990, 12,52-79.[4]冯大政,焦李成,保铮.动态分布参数神经网络及其稳定性分析. 1994年中国神经网络大会论文集.武汉:1-4.[5][5][6]廖晓昕著.稳定性的数学理论及应用.武汉:华中师范大学出版社,1988, 7, 79-83. -
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