Sequences of Global Bifurcations and the Related Outcomes after Crisis of the Resonant Attractor in a Nonlinear Oscillator

Abstract

The problem of the system behavior after annihilation of the resonant attractor in the region of the nonlinear resonance hysteresis is considered. The sequences of global bifurcations, in connection with the associated metamorphoses of basins of attraction of coexisting attractors, are examined. The study allows one to reveal the mechanism that governs the phenomenon of the post crisis ensuing transient trajectory to settle onto one or another remote attractor. The problem is studied in detail for the twin-well potential Duffing oscillator. The boundary which splits the considered region of system parameters into two subdomains, where the outcome is unique or the two outcomes are possible, is defined.