Nonlinear Differential Equation Reconstruction and Taken’s Embedding Theorem

Salt Lake Community College

The considerable usefulness of differential equations in modeling physical system dynamics is limited by the ability to generate equations which accurately reproduce observed behavior. Especially in the case of nonlinear systems, finding such a set of differential equations can be a nontrivial problem. However, there are numerical methods for generating differential equations to model empirical data. This paper briefly outlines the trajectory method of Perona et al. for fitting a system of differential equations to time series data. The basis of the system of equations needed to optimize the model are given. Creation of an algorithm to implement the method is discussed. The ability of the algorithm to reconstruct nonlinear systems with chaotic behavior is demonstrated. This method has great flexibility, allowing for direct application to the analysis of many systems without requiring prior knowledge of the underlying mechanisms.