Determining Mixed Linear-Nonlinear Coupled Differential Equations fromMultivariate Time Series Data

摘要

A new method is described for extracting mixed linear-nonlinear coupleddifferential equations from multivariate time series data. A tractable hierarchy of moment equations is generated by operating on a suitably truncated Volterra functional expansion. The hierarchy facilitates the calculation of the coefficients of the coupled differential equations. In order to demonstrate the methods ability to accurately estimate the coefficients of the governing differential equations the method is applied to data derived from the numerical solution of the Lorentz equations with additive noise. The method is then used to