Fractals in neurodynamics: From hybrid dynamical systems point of view

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.