Qualitative Behavior of Rational Difference Equation of Big Order

Abstract

We investigate the global convergence, boundedness, and periodicity of solutions of the recursive sequence xn+1=axn-l+bxn-x/c+dxn-lxn-k, n=0,1,…, where the parameters a, b, c, and d are positive real numbers, and the initial conditions x-t,x-t+1,…,x-1 and x0 are positive real numbers where t=maxk,l.