Fast analysis algorithm for hysteresis neural networks and its application for classification of chaos

This article proposes an efficient algorithm to analyze dynamics from piecewise linear hysteresis neural networks (ab.HNN). The algorithm uses piecewise linear exact solutions and can calculate the solutions of the HNN and its Lyapunov exponents accurately and speedily. The algorithm is available to clarify the following: the estimation of the domain of attraction to stable equilibria, the identification and the stability check of periodic orbits, and the confirmation of chaos generation. Especially, we apply this algorithm for classification of chaos from a simple hysteresis network (ab.SHN) which has only three parameters. Even in this simple case, the SHN exhibits complicated phenomena. These complicated phenomena can be observed in the laboratory experiments. Then we classify the complicated phenomena by using Lyapunov exponents which are calculated by our novel algorithm. We have discovered that the 5 cells SHN exhibits area expanding chaos and 3, 4, 5-dimensional volume expanding chaos in phase space