Global Behavior of a Rational Difference Equation

Abstract:

In this paper, we determine the forbidden set, introduce an explicit formula for the solutions, and discuss the global behavior of a rational difference equation x_(n+1)=(x_n x_(n-k))/(αx_n+βx_(n-(k+1)) ), where inter k∈N, inter n∈N∪{0},α,β are real numbers, the initial conditions (x_(-(k+1) ),x_(-k),⋯,x_0 )∈R^(k+2).