Global Attractivity and Periodic Character of Difference Equation of Order Four

Abstract EN

We investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence xn+1=axn+((bxn-1+cxn-2+dxn-3)/(αxn-1+βxn-2+γxn-3)), n=0,1,…, where the parameters a,b,c,d,α,β, and γ are positive real numbers and the initial conditions x-3,x-2,x-1, and x0 are positive real numbers.