May’s Host–Parasitoid geometric series model with a variable coefficient

During the last fifteen years there has been a significant growth of mathematical and scientific interest related to the study of difference equations with variable coefficients. The reason might as well be that variable coefficients make several scientific models more realistic. The question, usually asked, is about the effect on the dynamics of a difference equation, after imposing variability on one or more of the coefficients of the equation. In this article, we investigate the boundedness and in some cases, the global behavior of solutions of a system of rational difference equations with a variable coefficient. If the coefficient is constant, then, up to an appropriate change of variables, the system that we study is the geometric series case of May’s Host–Parasitoid Model.