Dual-moon forced dynamics and nonlinear aggregation in Saturn’s F ring: from quasi-periodicity to modulated oscillations

We develop a minimal nonlinear model to investigate the oscillatory dynamics of Saturn’s F ring under dual-moon forcing from Prometheus and Pandora. The model extends classical predator–prey dynamics by incorporating both a nonlinear mass aggregation term $$kM^n$$ and explicit dual-frequency forcing, capturing how higher-order coagulation physics interacts with multi-moon perturbations. Through systematic numerical integration and dynamical-systems tools, including time-series, spectral, stroboscopic, and rotation number analysis, we identify distinct dynamical regimes controlled by the parameters n and k. For moderate nonlinearity $$(n=1.28, k=0.54)$$ , the numerical diagnostics are consistent with bounded quasiperiodic motion, characterized by smooth amplitude modulation, thin stroboscopic loops, and discrete spectral peaks. For stronger nonlinearity $$(n=1.30, k=0.62)$$ , the same diagnostics indicate a transition toward strongly modulated oscillations, with broadened stroboscopic bands and sideband-rich spectra. A projected rotation-number diagnostic reveals organized regions in parameter space, including smooth quasiperiodic-like domains and near-locking bands analogous to Arnold tongues. Our results show that a reduced deterministic dual-forcing model can generate bounded quasiperiodic-like and strongly modulated aggregation-fragmentation cycles with timescales comparable to relevant moon-ring forcing periods, providing a possible low-dimensional mechanism contributing to F-ring variability.