| Abstract: | Recently, hybrid dynamical systems have attracted considerable attention in the automatic control domain. In this article, a theory for recurrent neural networks is presented from a hybrid dynamical systems point of view. The hybrid dynamical system is defined by a continuous dynamical system discretely switched by external temporal inputs. The theory suggests that the dynamics of continuous-time recurrent neural networks, which are stochastically excited by external temporal inputs, are generally characterized by a set of continuous trajectories with a fractal-like structure in hyper-cylindrical phase space. This work was presented, in part, at the 7th International Symposium on Artificial Life and Robotics, Oita, Japan, January 16–18, 2002 |
