Dynamic Hysteresis
Collapse of $M$ leads to loss of internal structure.
Recovery is delayed because feedback disappears.
Order Parameters
$\pi_{int}$ (Metabolism) |
$M$ (Total Info)
Current $\pi_{int}$: 2.000
Phase Portrait ($\pi_{int}$ vs $M$)
x-axis: $\pi_{int}$ | y-axis: $M$
Governing Equations (CFD v14d)
Eq.(1)
① Evolution of density field $\rho$
$$ \frac{\partial \rho}{\partial t} = -\nabla\cdot(\rho\mathbf{v}) + D_{mask}\nabla^2\rho + (\pi_{int}-\lambda_0)\rho - \kappa\rho^2 $$
Eq.(7)(8)
② Dynamics of Internal Metabolism $\pi_{int}$
$$ \frac{d\pi_{int}}{dt} = -k_{drug}(\pi_{int} - \pi_{tgt}) + k_{rec}(\pi_{base} - \pi_{int}) + k_{fb}M $$
Eq.(2)
③ Markov Blanket Flux (at $r=1$)
$$ -\mathbf{n}\cdot\left(\rho\mathbf{v} - D_{mask}\nabla\rho\right) = \pi_{ext}\cdot I(\theta,t) - \pi_{act} R \rho $$
Eq.(3)(4)
④ Flow velocity & defensive viscosity
$$ \mathbf{v} = -\frac{B}{\gamma(G)}\nabla F, \quad \gamma(G) = \gamma_{min} + \frac{\gamma_{max}-\gamma_{min}}{1+e^{-a(G-G_{th})}} $$
Eq.(5)
⑤ Transformation resistance
$$ G[\rho,F] = k_G \int_0^{2\pi}\int_0^1 \rho F r\,dr\,d\theta $$
Eq.(6)
⑥ Dynamic Potential $F$ (Erosion)
$$ \frac{\tau_{base} R / (r+r_0)}{1+\rho/\rho_0} \frac{\partial F}{\partial t} = -(F-F_0) - \int W \rho \, d\beta' $$