随机扰动下细胞神经网络的亚稳定性.pdfVIP

A b str a c t S ince cellu lar n eural netw orks (C N N s) w ere introduced by L . O . C hua and L . Y ang in 1988, its stab ility h as b een investigated in m any p ap ers due to its im p ortant app lication in sign al processin g , p attern recogn ition an d m any oth er fields. Ivletastab ility is kn ow n as th e ph enom en on th at a m u lti-stab le sy stem m ay have tran sition s b etw een d ifferent stab le states u n der ran dom p erturbation s of prop er inten sity. In th is pap er, w e m ake a m etastab ility an alysis of cellu lar n eural n etw ork s w ith m u lti-stab le equ ilibria an alyt- ically an d num erically. V ia th e large dev iation th eory, w e can d efin e th e M O ST stab le equ ilibriu m accord in g to th e m in im um action fu n ction al of th e tran sition p ath s b etw een these equ ilibria. U n der a proper inten sity of w h ite noise, the trajectories from any in itial position w ill go and stay near the m ost stab le equ ilibria or their attractin g b asins. W e prov ide a sufficient con dition to find th e m ost stab le equ ilib rium by estim ating an d com ? paring th e m in im al valu e of the action function al in th e ran dom p erturb ation th eory. In addition , w e give a sim u lation of 2-d im en sional C N N system to illu strate th e th eoretical re su lt . K ey W ord s: C ellu lar N eural N etw orks. R an dom P erturb ation , M etastab ility, A ction F u n ction al, L arge D ev iation T h eory. C h in ese L ib rary C la ssifica tio n : 0 175 .1 ii 主 要 符 号对 照 表 函数u⑴关于时间求导 R n n 维 欧 氏空 间 II- Hi 空 间 中一 ^t?向量 1-范数 II ? lb 空 间 中一个 向量 2-范数 ^  e {- 1,0.1} 指标 向量 《对应 的7?”中的子 区域 % 中的平衡点 平 衡 点M 的吸 引域 d B 区域 B 的边 界 《的相邻指标集，n . { 《g {- i;o, I}1 ：| |n iii 1} A