On a System of k-Difference Equations of Order Three

Abstract EN

In this paper, we deal with the global behavior of the positive solutions of the system of k-difference equations un+11=α1un−11/β1+α1un−22r1, un+12=α2un−12/β2+α2un−23r2,…, un+1k=αkun−1k/βk+αkun−21rk,n∈ℕ0, where the initial conditions u−lil=0,1,2 are nonnegative real numbers and the parameters αi,βi,γi, and ri are positive real numbers for i=1,2,…,k, by extending some results in the literature.

By the end of the paper, we give three numerical examples to support our theoretical results related to the system with some restrictions on the parameters.