On the recursive sequence xn+1 = α+βxn/Bxn+Cxn-1
Date of Original Version
The global character of solutions of a recursive sequence were investigated. The parameters and initial conditions of the nonlinear, second order and rational difference equation were nonnegative and positive, respectively. The semicycles of solutions were described and global asymptotic stability of the equilibrium of the equation was proved.
Nonlinear Analysis, Theory, Methods and Applications
Cunningham, K., M. R.S. Kulenović, G. Ladas, and S. V. Valicenti. "On the recursive sequence xn+1 = α+βxn/Bxn+Cxn-1." Nonlinear Analysis, Theory, Methods and Applications 47, 7 (2001): 4603-4614. doi:10.1016/S0362-546X(01)00573-9.