Theoretical analysis reveals conditions for phase-locking and stability in degenerate resonance under decaying perturbations, indicating mechanisms of permanent resonance capture.
The effect of damped oscillating perturbations on nonisochronous systems on the plane is studied. It is assumed that the intensity of perturbations decays with time as a power law, and the frequency is asymptotically constant with limit value satisfying a degenerated resonance condition. Solutions of perturbed equations in the phase-locking regime with near-resonance amplitude are also studied. A model system describing a capture in a degenerated resonance is described via averaging methods. Conditions for existence and stability of resonance solutions are given. The stability is verified by constructing appropriate Lyapunov functions.
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О. А. Султанов (2026) studied this question.
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