The _dynamics_ of the system is expressed by the two time series \$$X[t]\$$ and \$$X_2[t]\$$.

Intuitively, we would expect that given a starting state \$$S[0] = (X[0], X_2[0])\$$, it will eventually approach some limiting state \$$S[{\infty}] = (X', X_2')\$$ as \$$t\$$ advances - that is the _equilibrium_ state towards which it is bound.