Title

Global dynamics of perturbation of certain rational difference equation

Document Type

Article

Date of Original Version

1-1-2019

Abstract

We investigate the global asymptotic stability of the difference equation of the form x n+1 = Ax n2 + F/ax n2 + ex n-1 ; n = 0, 1, . . ., with positive parameters and nonnegative initial conditions such that x 0 +x -1 > 0. The map associated to this equation is always decreasing in the second variable and can be either increasing or decreasing in the first variable depending on the parametric space. In some cases, we prove that local asymptotic stability of the unique equilibrium point implies global asymptotic stability.

Publication Title

Turkish Journal of Mathematics

Volume

43

Issue

2

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