P-bifurcation: the stationary PDF changes shape (unimodal → bimodal). Occurs when noise pushes a system across a deterministic fixed point.
D-bifurcation: the top Lyapunov exponent λ changes sign (λ<0 → stable, λ>0 → stochastic chaos).
For pitchfork: p*(x) ∝ exp(μx²/σ² − x⁴/(2σ²)). Above μ=0: bimodal (P-bifurcation). The Lyapunov exponent λ = μ − 3⟨x²⟩.
Top panel: particle trajectories. Bottom panel: empirical PDF (histogram).