THE COEXISTENCE OF PERIODIC, ALMOST-PERIODIC AND CHAOTIC ATTRACTORS IN THE VAN-DER-POL-DUFFING OSCILLATOR

In this paper are presented the computer simulation and the approximat e theoretical analysis of the behaviour of the van der Pol-Duffing for ced oscillator at the passage through principal resonance, at increasi ng and decreasing driving frequency. Almost-periodic oscillations, fre quency locking, transition to chaotic motion and the jump from the non -resonant to the resonant state are observed and interpreted in the li ght of approximate analytical theory and by the use of topological con cepts. (C) 1997 Academic Press Limited.