Parameter and Structure Inference for Nonlinear Dynamical Systems

A great many systems can be modeled in the nonlinear dynamical systems framework, as (x) over circle = f(x) + xi(t), where f () is the potential function for the system, and 4 is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We use the Bayesian Information Criteria (BIC) to rank models, together with the beam search to search the space of models. We show that we can accurately determine the structure of simple nonlinear dynamical system models, and the structure of the coupling between nonlinear dynamical systems where the individual systems are known. This last case has important ecological applications.