Stability of Nonhyperbolic Equilibrium Solution of Second Order Nonlinear Rational Difference Equation

Abstract

This is a continuation part of our investigation in which the second order nonlinear rational difference equationxn+1=(α+βxn+γxn-1)/(A+Bxn+Cxn-1),n=0,1,2,…, where the parametersA≥0andB,C,α,β,γare positive real numbers and the initial conditionsx-1,x0are nonnegative real numbers such thatA+Bx0+Cx-1>0, is considered. The first part handled the global asymptotic stability of the hyperbolic equilibrium solution of the equation. Our concentration in this part is on the global asymptotic stability of the nonhyperbolic equilibrium solution of the equation.