On the architecture of a recurrent neural network as a chaos 1/f generator

We have developed an original recurrent neural network architecture (“n-variable unlimited recurrent adjustable network” (URAN_n)) which is composed of two layer artificial neuron groups connected by the feedforward and feedback connection. Each feedback connection has time delay unit while the feedforward portion does not have them. In this study, we have derived several formulae to determine the inner parameters of URAN_n, from the qualitative analysis on its continuous dynamical systems considering the geometrical structure of the stationary solution (or the equilibrium state) and the flow speed ratio of the vector field. By adjusting the parameters in URAN₂ under constraint of design formulae derived, we have generated chaotic time series using modified Rossler´s constraint model. Further, we have found 1/f-like fluctuation in the temporal signal generated from URAN_n. We have also shown an application of this fluctuation for the two-dimensional spatial pattern design