Nonlinear Mode Coupling — Internal Resonance (Duffing)

Two coupled Duffing oscillators exhibit internal resonance when their natural frequencies satisfy a ratio like 1:3, enabling energy transfer between modes that would be impossible in linear systems. The slow envelope dynamics govern intermittent bursts of amplitude exchange between the two modes.

Parameters
Mode 1: ω₁=1.0 (orange)
Mode 2: ω₂=3.0 (cyan)
Internal resonance: ω₂≈3ω₁
Energy exchange period