Global Dynamics of Some 3 × 6 Systems of Exponential Difference Equations

Abstract EN

We study the global dynamics of a list of following 3×6 systems of exponential difference equations: xn+1=α4+β4e-yn/γ4+yn-1, yn+1=α5+β5e-zn/γ5+zn-1, zn+1=α6+β6e-xn/γ6+xn-1, xn+1=α7+β7e-zn/γ7+zn-1, yn+1=α8+β8e-xn/γ8+xn-1, zn+1=α9+β9e-yn/γ9+yn-1, xn+1=α10+β10e-xn/γ10+xn-1, yn+1=α11+β11e-yn/γ11+zn-1, zn+1=α12+β12e-zn/γ12+yn-1, xn+1=α13+β13e-xn/γ13+zn-1, yn+1=α14+β14e-yn/γ14+yn-1, zn+1=α15+β15e-zn/γ15+xn-1, xn+1=α16+β16e-xn/γ16+yn-1, yn+1=α17+β17e-yn/γ17+xn-1, zn+1=α18+β18e-zn/γ18+zn-1, where αi,βi,γi,i=4,5,⋯,18 and the initial conditions x0,x-1,y0,y-1,z0,z-1 are arbitrary nonnegative real numbers.

This proposed work is considerably extended and improve some existing results in the literature.

Some numerical examples are given to not only verify our theoretical results but also provide different types of qualitative behavior of solution of these systems.