Fractal Basin Boundaries — Duffing Oscillator

Basins of attraction for ẍ − x + x³ = γcos(ωt) − δẋ

Parameters

0.30
0.15
1.00
80
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Duffing Basins:
The Duffing oscillator has two stable fixed points near x=±1. For each initial condition (x₀,ẋ₀), we integrate forward to determine which attractor the trajectory reaches. Blue = attractor at +1, red = attractor at −1. At the boundary, the fractal structure has the Wada property: every boundary point is on the boundary of all basins simultaneously. The fractal dimension of the boundary d_f > 1.