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Symmetry
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Difference Equations, Symmetric, Close to Symmetric and Cyclic Systems of...
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Difference Equations, Symmetric, Close to Symmetric and Cyclic Systems of Difference Equations

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (30 August 2018) | Viewed by 14353

Special Issue Editor

Prof. Dr. Stevo Stević

grade E-Mail Website
Guest Editor
Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, Serbia
Interests: complex analysis; difference equations; functional analysis; mathematical analysis; operator theory

Special Issue Information

Dear Colleagues,

There has been great recent interest in investigating the solvability and long-term behavior of solutions to linear and nonlinear difference equations and systems of difference equations of various types. One of the reasons for the interest is potential application of the methods, ideas and results related to the equations and systems of equations in some other branches of sciences, such as ecology, economics, biology, physics, population theory, etc. The mid-1990s started a considerable interest in concrete nonlinear difference equations and systems. If a difference equation is defined through a function of two variables, it is natural to form and study the corresponding two-dimensional symmetric system of difference equations, as well as some related systems, which are called close to symmetric systems of difference equations. In a similar way, cyclic systems of difference equations can be formed. This Special Issue is devoted to these and some related areas, which are popular nowadays.

Prof. Stevo Stevic
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Linear and nonlinear difference equations
  • Symmetric systems of difference equations
  • Close to symmetric systems of difference equations
  • Cyclic systems of difference equations
  • Partial difference equations
  • Solvable difference equations and systems
  • Long-term behavior of solutions
  • Equations and systems in the complex domain
  • Applications of difference equations and systems

Published Papers (5 papers)

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Research

14 pages, 241 KiB  
Article
Nonoscillatory Solutions to Second-Order Neutral Difference Equations
by Małgorzata Migda and Janusz Migda
Symmetry 2018, 10(6), 207; https://doi.org/10.3390/sym10060207 - 08 Jun 2018
Cited by 5 | Viewed by 2156
Abstract
We study asymptotic behavior of nonoscillatory solutions to second-order neutral difference equation of the form: [...] Read more.
We study asymptotic behavior of nonoscillatory solutions to second-order neutral difference equation of the form: Δ ( r n Δ ( x n + p n x n − τ ) ) = a n f ( n , x n ) + b n . The obtained results are based on the discrete Bihari type lemma and a Stolz type lemma. Full article
(This article belongs to the Special Issue Difference Equations, Symmetric, Close to Symmetric and Cyclic Systems of Difference Equations)
9 pages, 223 KiB  
Article
Stability of the Non-Hyperbolic Zero Equilibrium of Two Close-to-Symmetric Systems of Difference Equations with Exponential Terms
by Chrysoula Mylona, Nikolaos Psarros, Garyfalos Papaschinopoulos and Christos Schinas
Symmetry 2018, 10(6), 188; https://doi.org/10.3390/sym10060188 - 31 May 2018
Cited by 12 | Viewed by 3041
Abstract
In this paper, we study the stability of the zero equilibria of two close-to-symmetric systems of difference equations with exponential terms in the special case in which one of their eigenvalues is equal to − 1 and the other eigenvalue has an absolute [...] Read more.
In this paper, we study the stability of the zero equilibria of two close-to-symmetric systems of difference equations with exponential terms in the special case in which one of their eigenvalues is equal to − 1 and the other eigenvalue has an absolute value of less than 1. In the present study, we use the approach of center manifold theory. Full article
(This article belongs to the Special Issue Difference Equations, Symmetric, Close to Symmetric and Cyclic Systems of Difference Equations)
260 KiB  
Article
General k-Dimensional Solvable Systems of Difference Equations
by Stevo Stević
Symmetry 2018, 10(1), 8; https://doi.org/10.3390/sym10010008 - 28 Dec 2017
Cited by 2 | Viewed by 2741
Abstract
The solvability of a k-dimensional system of difference equations of interest, which extends several recently studied ones, is investigated. A general sufficient condition for the solvability of the system is given, considerably extending some recent results in the literature. Full article
(This article belongs to the Special Issue Difference Equations, Symmetric, Close to Symmetric and Cyclic Systems of Difference Equations)
325 KiB  
Article
Bounded Solutions to Nonhomogeneous Linear Second-Order Difference Equations
by Stevo Stević
Symmetry 2017, 9(10), 227; https://doi.org/10.3390/sym9100227 - 14 Oct 2017
Cited by 28 | Viewed by 2952
Abstract
By using some solvability methods and the contraction mapping principle are investigated bounded, as well as periodic solutions to some classes of nonhomogeneous linear second-order difference equations on domains N 0 , Z ∖ N 2 and Z . The case when the [...] Read more.
By using some solvability methods and the contraction mapping principle are investigated bounded, as well as periodic solutions to some classes of nonhomogeneous linear second-order difference equations on domains N 0 , Z ∖ N 2 and Z . The case when the coefficients of the equation are constant and the zeros of the characteristic polynomial associated to the corresponding homogeneous equation do not belong to the unit circle is described in detail. Full article
(This article belongs to the Special Issue Difference Equations, Symmetric, Close to Symmetric and Cyclic Systems of Difference Equations)
256 KiB  
Article
Solvable Three-Dimensional Product-Type System of Difference Equations with Multipliers
by Stevo Stević
Symmetry 2017, 9(9), 195; https://doi.org/10.3390/sym9090195 - 16 Sep 2017
Viewed by 2805
Abstract
The solvability of the following three-dimensional product-type system of difference equations [...] Read more.
The solvability of the following three-dimensional product-type system of difference equations x n + 1 = α y n a z n − 1 b , y n + 1 = β z n c x n − 1 d , z n + 1 = γ x n f y n − 1 g , n ∈ N 0 , where a , b , c , d , f , g ∈ Z , α , β , γ ∈ C \ { 0 } and x − i , y − i , z − i ∈ C \ { 0 } , i ∈ { 0 , 1 } , is shown. This is the first three-dimensional system of the type with multipliers for which formulas are presented for their solutions in closed form in all the cases. Full article
(This article belongs to the Special Issue Difference Equations, Symmetric, Close to Symmetric and Cyclic Systems of Difference Equations)
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