  Reservoir computing has been shown to be a useful framework for predicting
critical transitions of a dynamical system if the bifurcation parameter is also
provided as an input. Its utility is significant because in real-world
scenarios, the exact model equations are unknown. This Letter shows how the
theory of dynamical system provides the underlying mechanism behind the
prediction. Using numerical methods, by considering dynamical systems which
show Hopf bifurcation, we demonstrate that the map produced by the reservoir
after a successful training undergoes a Neimark-Sacker bifurcation such that
the critical point of the map is in immediate proximity to that of the original
dynamical system. In addition, we have compared and analyzed different
structures in the phase space. Our findings provide insight into the
functioning of machine learning algorithms for predicting critical transitions.
