2025/11/27 by Deeb, Omar El
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Astro and Planetary Science #FOS: Physical sciences #General Physics (physics.gen-ph) #Geomagnetism and Paleomagnetism Studies #Quantum chaos and dynamical systems
paper · doi:10.48550/arxiv.2512.05984
openalex publication_date 2025/11/27 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28
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 kMn and explicit dual-frequency forcing, capturing how higher-order coagulation physics interacts with multi-moon perturbations. Through extensive numerical integration and dynamical systems analysis, including time-series, spectral, stroboscopic mapping, and rotation number diagnostics, we identify distinct dynamical regimes controlled by the parameters n and k. For moderate nonlinearity (n=1.28, k=0.54), the system exhibits regular quasi-periodic motion on a two-torus, characterized by smooth amplitude modulation and discrete spectral lines. As nonlinearity increases (n=1.30, k=0.62), the dynamics transition to strongly modulated oscillations with intermittent phase slips, broadened Poincaré bands, and sideband-rich spectra. A rotation number heatmap reveals organized structures in parameter space, with smooth quasi-periodic regions bounded by near-locking bands analogous to Arnold tongues. Our results demonstrate that the F ring's complex morphology can emerge from deterministic multi-frequency dynamics rather than stochastic processes, with the system operating near critical boundaries where small parameter variations can trigger macroscopic reorganization. The model provides a framework for understanding pattern formation in other driven granular systems while offering testable predictions for ring observations.