Artificial neural networks with nonlinear feedbacks

This paper analyzes the behavior of the single-layer neural network system with continuous variables and nonlinear feedbacks. We prove that the system under some assumptions has a unique equilibrium point. We investigate the stability of this point with the help of direct Liapunov method. To guarantee the stability of this point, it is necessary to accept a very strong assumption about the properties of the connection matrix A. We suggest to change the initial system by such a way that the new one has the same equilibrium point and this point will be asymptotically stable regardless of the properties of A. The new system is constructed from original one by adding some supplementary cross connections. Two versions of the system are investigated: with only linear cross connections and with linear cross connections together with sequential nonlinearities. In both cases we prove that the equilibrium point is globally asymptotically stable, i.e. the attraction domain of this point covers all space.