The further constraints are \( 0 \le W_{ij} \le 1 \) and \( 0 \le w_{j} \le 1 \).

• We can thus write the action of \( W \) as

$$ \begin{equation*} w_i(t+1) = \sum_jW_{ij}w_j(t), \end{equation*} $$ or as vector-matrix relation $$ \begin{equation*} \hat{w}(t+1) = \hat{W\hat{w}}(t), \end{equation*} $$ and if we have that \( ||\hat{w}(t+1)-\hat{w}(t)||\rightarrow 0 \), we say that we have reached the most likely state of the system, the so-called steady state or equilibrium state.