Global Dynamics of Solutions of A New Class of Rational Difference Equations

Year 2019, Volume: 7 Issue: 2, 380 - 387, 15.10.2019

Mehmet Gümüş

Abstract

The purpose of this paper is to investigate the global dynamics of solutions of the following delay nonlinear difference equation $$ x_{n+1}=a+\frac{bx_{n-k}}{x_{n-l}}+\frac{cx_{n-l}}{x_{n-k}}\text{, }n=0,1,... $$ where the parameters $a,b,c$ are non-zero real numbers, $k,l\in \mathbb{Z}% ^{+}$ and the initial values $x_{-\max \{k,l\}},...,x_{-1},x_{0}\in \mathbb{R} -\{0\}$. The results obtained here improve and generalize some known ones in the literature. Moreover, several numerical simulations are provided to support obtained results.

Keywords

Dynamics, two periodic solution, boundedness

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