Before revision:  Besides, we observe that the HH equations are quite flat outside the stiff period where RK2 method also allows a large time step. Thus, we adaptively assign the ETD2RK and RK2 schemes depending on the stiff and flat regimes to achieve optimal accuracy and efficiency . Compared with the regular RK2 method , our ETD2RK method can enlarge time steps and raise efficiency more than one order of magnitude while capturing excellent accurate traces of membrane potentials and spike times of HH neurons.
After revision:  Besides, we observe that the HH equations are quite different between the spike and non-spike regions. Here, we design a second-order adaptive exponential time differencing algorithm (AETD2) for the numerical evolution of HH neural networks . Compared with the regular RK2 method , our ETD2RK method can enlarge time steps and raise efficiency more than one order of magnitude while capturing excellent accurate traces of membrane potentials and spike times of HH neurons.