Time-independent theoretical framework for stroboscopic nonlinear dynamics based on time-nonlocal response

Recent experiments have demonstrated the ability to manipulate nonlinear interactions via time modulation, giving rise to the so-called stroboscopic nonlinearity. To date, however, this phenomenon has not been subjected to a rigorous theoretical analysis. In this work, we clarify the physical mechanism underlying stroboscopic nonlinear dynamics based on time-nonlocal response and establish an effective time-independent model under suitable modulation conditions. The proposed model almost exactly reproduces the full time-dependent dynamics in the quasi-steady state and significantly outperforms empirical descriptions used previously. Our results provide a clear physical picture of stroboscopic nonlinear dynamics, and can be extended to other systems with time-nonlocal response, establishing a general framework for engineering nonlinear interactions through temporal modulation.