The dynamics of the solutions of some difference equations
type: Item
instance of: scholarly article
title: The dynamics of the solutions of some difference equations
zbMATH Open document ID: 1248.39012
DOI: 10.1155/2012/475038
published in: Discrete Dynamics in Nature and Society
publication date: 2012-10-19T00:00:00Z
review text: Summary: This paper is devoted to investigate the global behavior of the following rational difference equation: \(y_{n+1} = \alpha y_{n-t}/(\beta + \gamma \sum^k_{i=0} y^p_{n-(2i+1)} \prod^k_{i=0} y^q_{n-(2i+1)})\), \(n = 0, 1, 2, \dots\), where \(\alpha, \beta, \gamma, p, q \in (0, \infty)\) and \(k, t \in \{0, 1, 2, \dots\}\) with the initial conditions \(x_0, x_{-1}, \dots, x_{-2k}, x_{-2\max \{k, t\} - 1} \in (0, \infty)\). We will find and classify the equilibrium points of the equations under studying and then investigate their local and global stability. Also, we will study the oscillation and the permanence of the considered equations.
Mathematics Subject Classification ID: 39A22
zbMATH DE Number: 6096228
zbMATH Keywords: global behavior
zbMATH Keywords: rational difference equations
zbMATH Keywords: local stability
zbMATH Keywords: global stability
Wikidata QID: Q58700582
author: H. El-Metwally
author: Ramzi Alsaedi
author: E. M. Elsayed
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/475038
OpenAlex ID: W1985834941
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description: scientific article; zbMATH DE number 6096228