Bifurcation and chaos in the double well Duffing-van der Pol oscillator: Numerical and analytical studies

摘要

The behaviour of a driven double well Duffing-van der Pol (DVP) oscillatorfor a specific parametric choice ($\mid \alpha \mid =\beta$) is studied. Theexistence of different attractors in the system parameters ($f-\omega$) domainis examined and a detailed account of various steady states for fixed dampingis presented. Transition from quasiperiodic to periodic motion through chaoticoscillations is reported. The intervening chaotic regime is further shown topossess islands of phase-locked states and periodic windows (including perioddoubling regions), boundary crisis, all the three classes of intermittencies,and transient chaos. We also observe the existence of local-global bifurcationof intermittent catastrophe type and global bifurcation of blue-sky catastrophetype during transition from quasiperiodic to periodic solutions. Using aperturbative periodic solution, an investigation of the various forms ofinstablities allows one to predict Neimark instablity in the $(f-\omega)$ planeand eventually results in the approximate predictive criteria for the chaoticregion.