Exponential stability of additive neural networks

Exponential and stochastic stabilities of additive neural networks are analyzed. The results are especially suitable for asymmetric neural networks. A constraint on the connection matrix has been founded under which the neural network has a unique and exponentially stable equilibrium. Given any real matrix, this constraint can be satisfied if the gain coefficients and resistances in the neural net circuit are suitably adjusted. A one-to-one and smooth map between input currents and the equilibria of the neural network can be set up. The uniqueness results can be applied to analyze the master/slave net. For the neural network disturbed by some noise, the stochastic stability of the network is also discussed