On GLOBAL TRANSVERSALITY AND TANGENCY IN A PERIODICALLY FORCED, DAMPED DUFFING OSCILLATOR

摘要

In this paper, the analytical conditions for global transversality and tangency of a 2-D nonlinear dynamical system are derived. Further, a periodically forced, damped Duffing oscillator with a separatrix is investigated as an application example. The corresponding analytical conditions for the global transversality and tangency to the separatrix are obtained and the global and tangential flows are illustrated to verify the analytical conditions. The illustrations show that the analytical and numerical predictions of the global transversality and tangency exactly are agreed very well. The analytical conditions are obtained from the new theory rather than the Melnikov method. The new conditions for the global transversality and tangency are more accurate and independent of the small parameters. Therefore, chaotic flows based on the global transversality will be further investigated, and the corresponding results will be presented in a sequel.