Rate of convergence of solutions of rational difference equation of second order

S Kalabušić, MRS Kulenović
2004 Advances in Difference Equations  
We investigate the rate of convergence of solutions of some special cases of the equation x n+1 = (α + βx n + γx n−1 )/(A + Bx n + Cx n−1 ), n = 0,1,..., with positive parameters and nonnegative initial conditions. We give precise results about the rate of convergence of the solutions that converge to the equilibrium or period-two solution by using Poincaré's theorem and an improvement of Perron's theorem.
doi:10.1155/s168718390430806x fatcat:sz6njtozyjhkpjxiwdn2apnvym