Robust uniform persistence in discrete and continuous nonautonomous systems

Abstract

This is an extension of the work in Salceanu (2011) [14] to nonautonomous systems of difference and differential equations on the positive cone of Rm that exhibit a positively invariant boundary hyperplane X. It is shown that when a compact subset of X, which attracts all orbits in X, is a robust uniform weak repeller, robust uniform persistence for the complementary dynamics (i.e., the dynamics in Rm∖X) is obtained. Additional assumptions are made, to deal with the nonautonomous nature of the systems. Some particular cases that often occur in applications are discussed and then sufficient conditions for the robust uniform persistence of the disease in two epidemic models from the literature are given.