Dynamics of a Higher-Order Three-Dimensional Nonlinear System of Difference Equations

Abstract

In this paper, we study the semi-cycle analysis of positive solutions and the asymptotic behavior of positive solutions of three-dimensional system of difference equations with a higher order under certain parametric conditions. Furthermore, we show the boundedness and persistence, the rate of convergence of the solutions and the global asymptotic stability of the unique equilibrium point of the proposed system under certain parametric conditions. Finally, for this system, we offer some numerical examples which support our analytical results.

Keywords

• system of rational difference equations of order <i>k</i> + 1
• semi-cycle analysis
• boundedness and persistence
• global asymptotic stability
• rate of convergence
• sequence analysis