q^{\uparrow}(t) =  f \, q^{\downarrow}(t)  - \tau \cdot \frac{ d q^{\uparrow}}{ dt }  - \gamma \cdot \frac{d p_{wf}}{dt}

\tau \geq  0 , \quad \gamma \geq 0,  \quad  0 \leq f \leq 1

q^{\uparrow}_n (t) +  \tau_n \cdot  \frac{ d q^{\uparrow}_n}{ dt }= \sum_m f_{nm} \cdot q^{\downarrow}_m(t)  - \gamma_n  \cdot  \frac{d p_n}{dt}

\tau_n \geq  0 ,  \quad \gamma_n \geq 0,  \quad f_{nm} \geq  0 , \quad \sum_i^{N^{\uparrow}} f_{nm} \leq 1

Q^{\uparrow}_n (t) = \sum_n f_{nm} Q^{\downarrow}_n(t)  - \tau_n \cdot \big[ q^{\uparrow}_n(t) - q^{\uparrow}_n(0) \big]  - \gamma_n \cdot \big[ p_n(t) - p_n(0) \big]

\tau_j \geq  0 ,  \quad \gamma_n \geq 0,  \quad f_{ij} \geq  0 , \quad \sum_i^{N^{\uparrow}} f_{ij} \leq 1

p_n(t) = p_n(0) - \tau_n / \gamma_n  \cdot \big[ q^{\uparrow}_n(t) - q^{\uparrow}_n(0) \big]  - \gamma_n^{-1} \cdot Q^{\uparrow}_n (t) + \gamma_n^{-1} \cdot \sum_m f_{nm} Q^{\downarrow}_m(t)