| Nonlinear phenomena arise in all fields of engineering, physics, chemistry, biology, economics, and sociology. Mathematical models are used to simulate the nonlinear behaviour of these systems. In this thesis a perturbation approach is used to analytically approximate the discrete return map of two representative nonlinear models; the Rossler and the Lorenz systems.;In numerous nonlinear models an analytical solution is impossible to be found therefore numerical methods are used to derive an approximate solution of the system. A perturbation approach based on the Poincare mapping technique, Floquet theory and a time-correction technique for perturbed limit cycles can be used to analytically approximate the numerical solutions for nonlinear and chaotic systems which do not have a simple analytical solution.;Standard Floquet theory is based on a linear approximation to perturbations of the limit cycle. In this work an extension of the Floquet theory is used, along with a correction for the time needed for a perturbed limit cycle to reach the Poincare section for the first time, after some initial perturbations have been imposed to the system. This perturbation approach is then applied to Rossler's and Lorenz's models. (Abstract shortened by UMI.)... |
