Global Behavior of a New Rational Nonlinear Higher-Order Difference Equation

الملخص EN

Let k be a nonnegative integer and c a real number greater than or equal to 1.

We present qualitative global behavior of solutions to a rational nonlinear higher-order difference equation zn+1=(czn+zn-k+c-1znzn-k)/(znzn-k+c), n≥0, with positive initial values z-k,z-k+1,⋯,z0, and show the global asymptotic stability of its positive equilibrium solution.