Table 2.

Mathematical representation of cyber attack vectors.

$f_1\left(x_t\right)=\alpha \times x_t,$ $\alpha =$ random$\left(0.1-0.8\right)$

$f_2\left(x_t\right)=\left\{\begin{array}{c}0,\left(38\le x_t\le 43\right)\hfill \\ x_t,otherwise\hfill \end{array}\right.$

$f_3\left(x_t\right)={\lambda }_t\times x_t,{\lambda }_t=$ random$\left(0.1-0.8\right)$

$f_4\left(x_t\right)=\left\{\begin{array}{c}0,\left(x_t-{\lambda }_t\right)<0\hfill \\ \left(x_t-{\lambda }_t\right),otherwise\hfill \end{array}\right.$     ${\lambda }_t=random\left(0.1,max\left(X\right)\right)$

$f_5\left(x_t\right)=\left\{\begin{array}{c}{x}_t-mean(X),\left(x_t-mean(X)\right)\ge 0\hfill \\ x_t,otherwise\hfill \end{array}\right.$

$f_6\left(x_t\right)=x_{(49-t)},t=\left\{1,2,3,\dots ,48\right\}$