Global dynamics of perturbation of certain rational differenceequation

Authors

SABINA HRUSTIC
MUSTAFA KULENOVIC
SAMRA MORANJKIC
ZEHRA NURKANOVIC

DOI

10.3906/mat-1812-102

Abstract

We investigate the global asymptotic stability of the difference equation of the form \begin{equation*} x_{n+1}=\frac{A x_{n}^{2}+F}{a x_{n}^{2}+e x_{n-1}}, \quad n=0,1,\ldots, \end{equation*}% 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.

Keywords

Difference equation, attractivity, invariant, period doubling bifurcation, periodic solutions

First Page

894

Last Page

915

Recommended Citation

HRUSTIC, SABINA; KULENOVIC, MUSTAFA; MORANJKIC, SAMRA; and NURKANOVIC, ZEHRA (2019) "Global dynamics of perturbation of certain rational differenceequation," Turkish Journal of Mathematics: Vol. 43: No. 2, Article 23. https://doi.org/10.3906/mat-1812-102
Available at: https://journals.tubitak.gov.tr/math/vol43/iss2/23