Noise-Induced Phase Transition — Horsthemke-Lefever

Model Parameters

Drift a (bistability): 0.5

Noise Intensity σ²: 0.5

Noise Color τ (corr. time): 0.0

N Ensemble Particles: 200

Time Step dt: 0.01

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⟨x⟩

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Var(x)

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Phase

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PDF peaks

Horsthemke-Lefever model:
dx = (ax − x³)dt + σ·x·dW

The multiplicative noise (σ·x·dW) can induce a bimodal stationary distribution even when the deterministic system is monostable (a<0). Critical noise: σ²_c = 2|a|. Above σ²_c: new noise-induced phase appears. This is a purely stochastic phase transition — forbidden without fluctuations.