The conditions linking the strict selection property in continuous- and discrete-time dynamical systems on a standard simplex are investigated. These conditions permit choosing the integration step adequately without losing the strict selection property in the system. An attempt is made to link the concepts of selection for difference systems with the corresponding differential analog. It is shown that if the solution of a difference system uniformly converges to the vertex of the simplex, then the original differential systems possess the selection property as well and are widely used in constructing mathematical models of various real-world processes.
Kapitanov et al. (Mon,) studied this question.