Global dynamics of certain mix monotone difference equation
type: Item
instance of: scholarly article
title: Global dynamics of certain mix monotone difference equation
zbMATH Open document ID: 1441.39004
author: S. Kalabušić
author: Mehmed Nurkanovic
author: Zehra Nurkanović
published in: Mathematics
publication date: 2018-08-13T00:00:00Z
review text: Summary: We investigate global dynamics of the following second order rational difference equation \(x_{n + 1} = \frac{x_n x_{n - 1} + \alpha x_n + \beta x_{n - 1}}{a x_n x_{n - 1} + b x_{n - 1}},\) where the parameters \(\alpha, \beta, a, b\) are positive real numbers and initial conditions \(x_{- 1}\) and \(x_0\) are arbitrary positive real numbers. The map associated to the right-hand side of this equation is always decreasing in the second variable and can be either increasing or decreasing in the first variable depending on the corresponding parametric space. In most cases, we prove that local asymptotic stability of the unique equilibrium point implies global asymptotic stability.
Mathematics Subject Classification ID: 39A20
Mathematics Subject Classification ID: 39A23
Mathematics Subject Classification ID: 39A30
zbMATH DE Number: 6916885
zbMATH Keywords: difference equations
zbMATH Keywords: equilibrium
zbMATH Keywords: period-two solutions
zbMATH Keywords: period-four solutions
zbMATH Keywords: global stability
zbMATH Keywords: monotonicity
MaRDI profile type: Publication
full work available at URL: math6010010
OpenAlex ID: W2783415385
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DOI: 10.3390/MATH6010010
description: scientific article; zbMATH DE number 6916885