Model Dynamics
Temporal evolution equations governing frame selection, load dynamics, and the collapse mechanism.
Load Dynamics
Ornstein-Uhlenbeck process for cognitive load
dL(t) = −θ(L − L₀)dt + σdW(t)
θ: mean reversion rate
L₀: baseline load
σ: noise amplitude
W(t): Wiener process
L₀: baseline load
σ: noise amplitude
W(t): Wiener process
Frame Evolution
von Neumann equation for frame states
iℏ ∂|ψ⟩/∂t = [Ĥ₀ + κV]|ψ⟩
Ĥ₀: free Hamiltonian
V: interaction potential
κ: coupling constant
V: interaction potential
κ: coupling constant
Collapse Mechanism
Cognitive frame reduction
|ψ⟩ → Π_κ|ψ⟩ / ‖Π_κ|ψ⟩‖
Triggered when load L exceeds threshold L_crit.
Π_κ: projection onto selected frame.
Π_κ: projection onto selected frame.
Coupling Constant κ
FS-AC interaction strength
κ ∈ [0, 1]
κ = 0: no awareness (pure FS dynamics)
κ = 1: full AC dominance
Optimal range: 0.3 – 0.7
κ = 1: full AC dominance
Optimal range: 0.3 – 0.7
Simulation Parameters
θ = 0.15
Mean reversion
L₀ = 0.5
Baseline load
σ = 0.1
Noise amplitude
κ = 0.5
Coupling strength