Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

ni 1 = '1' output ( firing ).
Each neuron has a fixed threshold, say, thi for neuron 'i'. Each neuron
readjusts its states randomly by using the following equations.
For neuron i :
Output ni = 1 ; if ∑wij n j > thi
j≠i
= 0 ; otherwise (14.7)
The information storage for such a system is normally described by
s
ij i
where ni s represents set of states for s being an integer 1,2,....., n.
To analyze the stability of such a neural network, Hopfield proposed a special
kind of Liapunov energy function given in expression (14.8)
The change in energy ∆E due to change in the state of neuron 'i' by an amount
∆ nj is given by
As ∆ ni is positive only when the bracketed term is positive, thus any change in
E under the expression (14.9) is negative. Since E is bounded, so the iteration
of the Hopfield neural algorithm, given by the expression (14.8), must lead to
stable states.
Continuous Hopfield net
The continuous Hopfield net can be best described by the following
differential equation,
s
j
w = ∑ n − n −
s
( 2 1)( 2 1 )
E = − (1/2) Σ wij ni nj − Σ li ni + Σ thi nI . (14.8)
i≠j I j
∆ Ε = − ( Σ wij nj + li − thi ) ∆ ni (14.9)
i≠j
du
∑ wijn j −ui
R
i
C i = /
i + li
dt j
(14.10)