Parameter perturbations yielding infinitely many attractors in the forced damped pendulum

Identify explicit parameter values (perturbations) for the periodically forced damped pendulum θ¨ + γ θ˙ + sin θ = ρ cos t (considering the time-2π Poincaré return map) that produce infinitely many coexisting attractors, in particular determining such perturbations near the illustrated case γ=0.2 and ρ=2.

Background

The authors paper the forced damped pendulum with γ=0.2 and ρ=2, where numerics indicate two attracting fixed points and three chaotic saddles. By Newhouse’s results, small parameter changes can create infinitely many coexisting attractors, but the paper does not identify which specific perturbations produce this phenomenon for the pendulum model.

They explicitly note that they do not know which perturbations yield infinitely many attractors and reference prior work where such behavior is expected.