Study numerically the fluctuations in the process in Eq. (13.1) with (t) given by Eq. (13.2). Try, from the changing time dependence of the fluctuations

Study numerically the fluctuations in the process in Eq. (13.1) with η(t) given by Eq. (13.2). Try, from the changing time dependence of the fluctuations (the variance and the autocorrelations), to predict the transition taking place at time t∗ = 4000 where η(t) vanishes. You may find it difficult to obtain good forecasting efficiency.

Equation (13.1)

Equation (13.2)

x(t + 1) = x(t) n(t)x(t) +x(t),