Qualitative analysis of neural networks under structural perturbations

A qualitative analysis of Hopfield neural networks with unknown random structure is developed. Simple algebraic conditions are established for structural exponential stability of x=0 of the neural network and for an estimate of its domain. By using the natural form, the quadratic form, and maximum-type form of a Lyapunov function, three differential estimates of the domain D_e of structural exponential stability of x=0 of the neural network are given. Another simple algebraic condition presented guarantees the maximum possible estimate of D_e. In all the cases bounds on the motions of the neural network in a forced regime are provided without using any information about its unknown, random structure