Time series modeling and synchronization using neural networks

Abstract

In the last few years, neural networks have found interesting applications in the field of time series modeling and forecasting. Some recent results show the ability of these models to approximate the dynamical behavior of nonlinear chaotic systems, leading to similar dimensions and Lyapunov exponents. In this paper we analyze further the dynamical properties of neural networks when comparted with chaotic systems. In particular, we show that the possibility of synchronizing chaotic systems gives a natural criterion for determining similar dynamical behavior between these systems and neural approximate models. In particular we show that a neural model obtained from an experimental scalar laser-intensity time series can be synchronized to the time series, indicating that it captures the dynamical behavior of the system underlying the data.