An Analytical Method for Predicting Chaos in Perturbed Planar Non-Hamiltonian System

摘要

An analytical method for predicting chaos in perturbed planar non-Hamiltonian integrable systems with slowly varying parameters was developed. Based on the analysis of the geometric structure of unperturbed systems, the condition of transversely homoclinic intersection was given. The generalized Melnikov function of the perturbed systems, the condition of transversely homoclinic intersection was given. The generalized Melnikov function of the perturbed system was found by applying the theorem on the differentiability of ordinary differential equation solutions with respect to parameters.