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

Abstract

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.