Amplitude Death in Coupled Oscillators

Stuart-Landau oscillators coupled by diffusion — oscillation silenced by frequency mismatch

Parameters

Coupling K 1.00 Frequency mismatch Δω 0.50 Base frequency ω₀ 1.00 Nonlinearity γ 1.00

State

|A₁|-

|A₂|-

Mode-

AD boundary K_c-

Stuart-Landau oscillators: ż₁ = (μ + iω₁ − γ|z₁|²)z₁ + K(z₂−z₁), ż₂ = (μ + iω₂ − γ|z₂|²)z₂ + K(z₁−z₂). With μ=1 (growth rate), ω₁ = ω₀ + Δω/2, ω₂ = ω₀ − Δω/2. Amplitude death (AD): when coupling K and detuning Δω satisfy K > μ + (Δω/2)² / (4μ) (approximate), both amplitudes collapse to zero. The bifurcation diagram shows the AD region in K-Δω space (yellow = oscillating, dark = dead).