Determining a model for the time scaling of the dynamic aperture of a circular accelerator is a topic of strong interest and intense research efforts in accelerator physics. The motivation arises in the possibility of finding a method to reliably extrapolate the results of numerical simulations well beyond what is currently possible in terms of CPU time. In earlier work, a proposal for a model based on Nekhoroshev theorem and Kolmogorov–Arnold–Moser theory was made. This model has been studied in detail and proved successful in describing the evolution of the dynamic aperture in numerical simulations, however a number of shortcomings had been identified and new models are proposed in this paper, which solve the observed issues. The new models have been benchmarked against numerical simulations for a simple system, the 4D Hénon map, as well as a realistic, non-linear representation of the beam dynamics in the LHC at 6.5 TeV providing in both cases excellent results.