M.P. Joy (UK)
stochastic neural networks, exponential stability.
The stability analysis of neural networks is important in the
applications and has been studied by many authors. How
ever, only recently has the stability of stochastic models
of neural networks been investigated. In this paper we
analyse the global asymptotic stability of a class of neu
ral networks described by a stochastic difference equation,
in fact, a Markov chain with state space Rm
. If Xn is
the state of the neural network at time n, we prove that
under certain conditions, Xn ! 0, n ! 1, and are able
to bound sample Lyapunov exponents – it turns out that
our model is exponentially stable under these conditions.
Our results assume neither the symmetry of the intercon
nection weights, neither do we assume differentiability or
monotonicity of the activation functions.