On the dynamics of the nonlinear rational difference equation xn+1 = Axn + Bxn−k + Cxn−l + bxn−k/dxn−k − exn−l

In this article, we study the periodicity, the boundedness and the global stability of the positive solutions of the following nonlinear difference equationxn+1=Axn+Bxn-k+Cxn-l+bxn-kdxn-k-exn-l,n=0,1,2,… where the coefficients A,B,C,b,d,e∈(0,∞)A,B,C,b,d,e∈(0,∞), while k and l   are positive integers. The initial conditions x-l,…,x-k,…,x-1,x0x-l,…,x-k,…,x-1,x0 are arbitrary positive real numbers such that k