: $$d_{0}\left( {t + \Delta t} \right) = max\left\{ 0,\ {\ d}_{0}(t) + g\frac{b + v_{0}\left( t \right)}{s + v_{0}\left( t \right) + v_{0}\left( t \right)} + {N\left( {0,\sigma^{0}} \right)}_{0}(t) \right\}$$ $$d_{0}\left( {t + \Delta t} \right) = max\left\{ 0,\,{\ d}_{0}(t) + g\frac{b + v_{0}\left( t \right)}{s + v_{0}\left( t \right) + v_{0}\left( t \right)} + {N\left( {0,\sigma^{0}} \right)}_{0}(t) \right\}$$  The 