Global Dynamical Properties of Rational Higher-Order System of Difference Equations

Abstract

In this paper, global dynamical properties of rational higher-order system are explored in the interior of ℝ+3. It is explored that under certain parametric conditions, the discrete-time system has at most eight equilibria. By the method of linearization, local dynamics has been explored. It is explored that positive solution of the system is bounded, and moreover fixed point P000 is globally stable if α1/α2<1, α4/α5<1, α7/α8<1. It is also investigated that the positive solution of the system under consideration converges to P000. Lastly, theoretical results are confirmed by numerical simulation. The presented work is significantly extended and improves current results in the literature.