Symbolic and numerical analysis for studying complex nonlinear behavior
The technique of Carleman linearisation is used in order to derive an approximate solution of a nonlinear dynamical system (possibly depending on parameters) in terms of exponential polynomials. Using the associated variational equation approximations of the Lyapunov exponents of the system are obtained via a mixed symbolic-numerical approach. An implementation using Axiom and Fortran is described. As an example an apparently new critical value for the Lorenz system is computed. Unfortunately, the article is at many places rather sketchy, so that it is difficult to follow. Especially the interface between the symbolic and the numerical computations remains rather unclear. No comparison between the efficiency and accuracy of the new approach and traditional methods for determining Lyapunov exponents is done.
scientific article; zbMATH DE number 1310133