End-states

A simulation ends when both populations and their respective type distributions are stable; i.e no further change occurs given current conditions. More specifically, we use the RelTol method to decide if the absolute difference between the populations between time \(t\) and \(t-1\) are very small, less than \(10^{-\epsilon}\) (see reltol_exponential in “Table: Parameters”) where \(\epsilon=6\) in our default setting. End-states defined by unchanged variables are known as stationary points. Exceptionally, under certain parameter settings, the HPC model does not converge into a stationary point but enters an oscillatory state. To handle these rare cases and others producing extremely slow-paced dynamics, simulations are interrupted regardless of the conditions after a certain number of iterations (\(time_{max}\) or max_iterations).