Study of exponential stability of equilibrium neural networks

In this article, we consider the generalized Hopfield neural networks and some sufficient criteria are derived for study exponential stability of the equilibrium of Hopfield neural networks of the form C
_i
du
_i
/d
_t
=Σ
_j=1
ⁿ
T
_ij
v
_j
-u
_i
/R
_i
+Ii i=1,2,...,n. by means of Lyapunov method and some analysis techniques, in which v
_i
=(λ
_i
u
_i
), and T=[T
_ij
]
_n×n
is a connection matrix, not requiring symmetric and all output responses g
_i
(
_·
) are the same. C
_i
> 0, R
_i
> 0 and I
_i
are called the capacitance, the resistance and the network external current input constants respectively of the ith neuron. The criteria are easy to check and apply in practice.0