Definition of Term: Single step function

We consider dynamic simulators of the form that model the evolution of a state vector by iteratively applying a single step function. For example, suppose the dynamic simulator takes as inputs an initial state vector \(w_0\), a time series of forcing inputs \(a_1,\ldots,a_T\), and some constant parameters \(\phi\), to produce a time series output \(w_1,\ldots,w_T\). If the evolution of the time series \(w_1,\ldots,w_T\) is defined by the equation \(w_t=f(w_{t-1},a_t,\phi)\), then \(f(.)\) is known as the single step function.