Global stability and oscillation in nonlinear difference equations of population dynamics

In this paper, we study the qualitative behavior of solutions of the discrete population modelwhere <f>p∈(0,1)</f>, <f>q,r∈(0,∞)</f>, <f>p<q/r<1+p</f>, <f>m∈(0,∞)</f> and <f>k</f> is a nonnegative integer. We obtain sufficient and necessary conditions for the oscillation of all eventually positive solutions about the positive equilibrium. Furthermore, we also show that such model is uniformly persistent, and that all its eventually positive solutions are bounded. Finally, we prove that the unique positive equilibrium <f>x*</f> is globally asymptotically stable if and only if <f>x*</f> is locally asymptotically stable and provide sufficient condition for <f>x*</f> to be globally asymptotically stable. [Copyright &y& Elsevier]