BIFURCATION AND CHAOS IN THE DOUBLE-WELL DUFFING-VAN-DER-POL OSCILLATOR - NUMERICAL AND ANALYTICAL STUDIES

The behavior of a driven double-well Duffing-van der Pol oscillator fo r a specific parametric choice (\alpha\ = beta) is studied. The existe nce of different attractors in the system parameters f - omega domain is examined and a detailed account of various steady states for fixed damping is presented. The transition from quasiperiodic to periodic mo tion through chaotic oscillations is reported. The intervening chaotic regime is further shown to possess islands of phase-locked states and periodic windows (including period-doubling regions), boundary crisis , three classes of intermittencies, and transient chaos. We also obser ve the existence of local-global bifurcation of intermittent catastrop he type and global bifurcation of blue-sky catastrophe type during the transition from quasiperiodic to periodic solutions. Using a perturba tive periodic solution, an investigation of the various forms of insta bilities allows one to predict Neimark instability in the f - omega pl ane and eventually results in the approximate predictive criteria for the chaotic region.