A.4 Proof of Theorem 4

A.4 Proof of Theorem 4
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A.4 定理 4 的证明

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发表时间:
1994
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通讯作者:
U. Zimmermann
U. Zimmermann
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作者:
U. Zimmermann

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(8)我们得到鬼吸引子G(c)由G(c)i = Xp x x c i给出:(19)对应于c的区域R(c)由所有aerent输入向量a组成,使得g(a i?其中g是Heavyside阶跃函数。将(19)式代入(20)式,我们可以看到,G(c)要位于区域R(c)中,我们必须有Xp x x c i?如果c i = 1,则X k z k > 0(21),如果c i = 0,则相反的不等式。设C i为节点i检测到的类别。
(8) we have that the ghost attractor G(c) is given by G(c) i = X p x x c i : (19) The region R(c) corresponding to c consists of all aaerent input vectors a such that g(a i ? X j z j) = c i ; (20) where g the Heavyside step function. Substituting (19) into (20) we see that for G(c) to lie in the region R(c) we must have X p x x c i ? X k z k > 0 (21) if c i = 1 and the opposite inequality if c i = 0. Let C i be the category detected by node i.