Maximum entropy approach to nonlinear modeling

We present a technique for building deterministic models of the nonlinear d ynamics underlying observed time series. It is formulated from maximum entr opy principle within the framework of information theory. Two numerical exa mples of chaotic time series illustrate the method. Furthermore, the theory on which the method is based, provides an entropy-like quantity that chara cterizes the suitability of the model, It is defined over the space of para meters of the model. We illustrate, with two applications, how this entropy can be a useful tool for exploring the phase space, and establishing a cri terion for choosing a convenient parametrized functional form. (C) 2000 Els evier Science B.V. All rights reserved.