A dimensional analysis on chaotic neural networks
Tohru Ikeguchi, Susmu Itoh, Toshio Utsunomiya, Kazuyuki Aihara · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1990
Abstract We apply a dimensional analysis to a neural network model with chaotic dynamics, or a mathematical model of chaotic neural networks. First, Lyapunov spectra are examined to confirm existence of chaotic network behavior and to calculate the Lyapunov dimension. Then, the correlation dimension is estimated in the following three cases: (1) reconstruction from single variable time series, (2) observation in state subspaces and (3) observation of the macroscopic average activity. The results show good correlation dimension obtained by observation in state subspaces and the characteristics of the correlation dimension estimated by macroscopic observation.