Stabilizing Chaos in the Four-Body Problem: Alp's Elastic Dark Matter vs Newtonian Dynamics

This is an updated version with corrected simulation parameters, improved figures, and detailed interpretation. The work investigates the Alps Elastic Dark Matter (AEDM) model, which introduces an elastic force in addition to Newtonian gravity. By numerically integrating the system over 30 days and analyzing total energy, angular momentum, orbital structure, and frequency spectra, we demonstrate that the AEDM model suppresses chaos and establishes bounded quasi-periodic motion. A comparison with the purely Newtonian model reveals the stabilizing effect of elasticity in complex gravitational systems.