Higher order mass aggregation terms in a nonlinear predator-prey model maintain limit cycle stability in Saturn's F ring

TL;DR

This paper introduces a novel predator-prey model with higher order mass aggregation terms to explain the stable oscillatory clumping behavior observed in Saturn's F ring, demonstrating how physical interactions maintain limit cycle stability.

Contribution

It develops a new nonlinear model incorporating higher order mass aggregation terms and analyzes its stability, revealing regimes of cyclic and non-cyclic behavior relevant to Saturn's F ring.

Findings

Limit cycle oscillations are stable within certain parameter ranges.

Phase transitions occur between cyclic and non-cyclic regimes.

Higher order mass terms are crucial for maintaining observed clumping dynamics.

Abstract

We consider a generic higher order mass aggregation term for interactions between particles exhibiting oscillatory clumping and disaggregation behavior in the F ring of Saturn, using a novel predator-prey model that relates the mean mass aggregate (prey) and the square of the relative dispersion velocity (predator) of the interacting particles. The resulting cyclic dynamic behavior is demonstrated through time series plots, phase portraits and their stroboscopic phase maps. Employing an eigenvalue stability analysis of the Jacobian of the system, we find out that there are two distinct regimes depending on the exponent and the amplitude of the higher order interactions of the nonlinear mass term. In particular, the system exhibits a limit cycle oscillatory stable behavior for a range of values of these parameters and a non-cyclic behavior for another range, separated by a curve across which phase transitions would occur between the two regimes. This shows that the observed clumping dynamics in Saturn's F ring, corresponding to a limit cycle stability regime, can be systematically maintained in presence of physical higher order mass aggregation terms in the introduced model.