On the stability of a Tank and Hopfield type neural network in the general case of complex eigenvalues

The stability of a Tank and Hopfield-type neural network is investigated for the general case of practically encountered complex eigenvalues sD of the matrix product DgT Df, where Dg and Df are approximations of the connection matrix D on the signal and constraint sides of the neural net, respectively. A stability criterion in the form of an analytic expression is derived, thus generalizing the results obtained by Yan (1991) for the special case of purely real eigenvalues.