Abstract:

Using the stable manifold theorem, we studied the local stability of two periodic positive solutions of second order rational nonlinear difference equationx_n+1=(a-bx_n)/(A+x_n-1),n=0,1,2,…where A,b>0,a≥0 were real numbers, and initial conditions x_-1 and x₀ were arbitrary positive real numbers. The results show that the positive equilibrium point of the second order nonlinear difference equation is stable, and the minimum two periodic positive solution is unstable.

Key words: second order, difference equation, two periodic solution, local asymptotic stability