Global asymptotic stability in a rational dynamic equation on discrete time scales

The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [15] in order to unify continuous and discrete analysis. The theory of dynamic equations not only unifies the theories of differential equations and difference equations, but also it extends these classical cases to cases in between, e.g., to so-called q-difference equations. Since then several authors have expounded on various aspects of this new theory, see the survey paper by Agarwal et al. [2] and the references cited therein.

Many other interesting time scales exist, and they give rise to many applications, among them the study of population dynamic models (see [8]). A book on the subject of time scales by Bohner and Petreson [5] summarizes and organizes much of the time scales calculus (see also [4]).