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Time-decaying perturbations of nonlinear oscillatory systems in the plane areconsidered. It is assumed that the unperturbed systems are non-isochronous andthe perturbations oscillate with an asymptotically constant frequency.Resonance effects and long-term asymptotic regimes for solutions areinvestigated. In particular, the emergence of stable states close to periodicones is discussed. By combining the averaging technique and stability analysis,the conditions on perturbations are described that guarantee the existence andstability of the phase-locking regime with a resonant amplitude. The resultsobtained are applied to the perturbed Duffing oscillator.

Nonlinear resonance in oscillatory systems with decaying perturbations