Resonance in coupled nonlinear oscillators with decaying perturbations

What the math gives to ML

The paper develops a constructive asymptotic normal-form procedure for coupled oscillators subject to perturbations that decay as powers of time. Its transferable mechanism is the removal of non-resonant, phase-dependent terms through homological equations of the form \(\omega_2(A)\partial_\varphi U_K=\text{forcing}\), while retaining averaged or resonant components that generate leading secular drift. This suggests a resonance-aware optimizer or recurrent-state update in which periodic modulation is transformed into slowly varying effective dynamics, with truncation order controlling a measurable residual error. The proposal is valuable only if experiments verify resonance peaks and the predicted power-law decay of the normal-form residual.