Global analysis of solutions of xn+1=βxn+δxn−2A+Bxn+Cxn−1

We study the global character of solutions of the third order rational difference equationxn+1=βxn+δxn−2A+Bxn+Cxn−1,n=0,1,…, where the parameters β, δ, A   are nonnegative, β+δ>0β+δ>0, B,C>0B,C>0, the initial conditions x−2,x−1,x0x−2,x−1,x0 are nonnegative real numbers and the denominator is always positive.