Behaviour of two-dimensional competitive system of nonlinear difference equations of higher order

We generalise a recent result of Mansour et al. (2012) and study other related systems that deal with the dynamics of a competitive population model described by a system of nonlinear difference equations. Particularly, we consider a discrete-competitive system of the form x(n+1) = f(x(n-(2k-1),) y(n-(k-1))), y(n+1) = g(x(n-(2k-1),) y(n-(k-1))), n is an element of N-0, where k is an element of N and f : R \ F-f -> R and g : R \ F-g -> R, where F-f and F-g denote the forbidden sets of f and g, respectively. This work, in turn, generalises several other results on system of nonlinear difference equations. See, for example, the work of Alghamdi et al. (2013), Elsayed (2012), Ibrahim et al. (2015), Kurbanli (2011) and Touafek and Elsayed (2012). Furthermore, the one-dimensional case of the given system provides a generalisation of a series of paper of Elsayed on nonlinear difference equations.