Influence of uncertainties and noise on basins/attractors topology and integrity of Duffing oscillator

Abstract

This work explores the influence of uncertainties and noise on the global dynamics of a well-known archetypal oscillator, namely the Duffing oscillator, with emphasis on the basins and attractors' topology and the dynamic integrity of coexisting solutions. To this aim, an adaptive phase-space discretization strategy is employed. Harmonic or parametric excitations with added noise and parametric uncertainty are considered, and their effects on the mean basins of attraction and attractors' distributions are observed. The time-dependency of stochastic responses is demonstrated, with long-transients influencing the long-term behavior. The effects of uncertainties and noise on the basins' areas, attractors’ distributions and basin boundaries are discussed. The probability distributions of the basins are then used to evaluate the dynamic integrity of the various coexisting solutions. The resulting integrity profiles can be employed for evaluating the safety of the oscillator under finite disturbances.