Global behaviour of solutions to a class of second-order rational difference equations when prime period-two solutions exist

2013 ◽  
Vol 19 (6) ◽  
pp. 898-926
Author(s):  
Sukanya Basu
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Rational Difference Equations ◽  
Global Behaviour ◽  
Prime Period ◽  
Period Two Solutions

On a recursive sequence

Kybernetes ◽  
2007 ◽  
Vol 36 (1) ◽  
pp. 98-115
Author(s):  
Mehdi Dehghan ◽  
Reza Mazrooei‐Sebdani
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Open Problem ◽  
Design Methodology ◽  
Initial Conditions ◽  
Open Problems ◽  
Content Type ◽  
Rational Difference Equations ◽  
Global Behaviour ◽  
Recursive Sequence

PurposeThe aim in this paper is to investigate the dynamics of difference equation yn+1=(pyn+yn−k)/(qyn+yn−k), n=0,1,2,… where k∈{1,2,3,…}, the initial conditions y−k, … ,y−1,y0 and the parameters p and q are non‐negative.Design/methodology/approachThe paper studies characteristics such as the character of semicycles, periodicity and the global stability of the above mentioned difference equation.FindingsIn particular, the results solve the open problem introduced by Kulenovic and Ladas in their monograph, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures.Originality/valueThe global behaviour of the solutions of equation yn+1=(pyn+yn−k)/(qyn+yn−k), n=0,1,2,… were investigated providing valuable conclusions on practical data.

scholarly journals On the Solutions of Four Second-Order Nonlinear Difference Equations

2019 ◽  
Author(s):  
İnci Okumuş ◽  
Yüksel Soykan
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Global Behavior ◽  
Nonlinear Difference Equations ◽  
Rational Difference Equations ◽  
The Stability

This paper deals with the form, the stability character, the periodicity and the global behavior of solutions of the following four rational difference equations x_{n+1} = ((±1)/(x_{n}(x_{n-1}±1)-1)) x_{n+1} = ((±1)/(x_{n}(x_{n-1}∓1)+1)).

scholarly journals On monotone solutions of some classes of difference equations

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
Stevo Stevic
Keyword(s):  
Difference Equations ◽  
Present Author ◽  
Second Order ◽  
Open Problems ◽  
Rational Difference Equations ◽  
Monotone Solutions

We describe a method for finding monotone solutions of some classes of difference equations converging to the corresponding equilibria. The method enables us to confirm three conjectures posed by the present author in a talk, which are extensions of three conjectures by M. R. S. Kulenović and G. Ladas,Dynamics of Second Order Rational Difference Equations. With Open Problems and Conjectures. Chapman and Hall/CRC, 2002. It is interesting that the method, in some cases, can be applied also when the parameters are variable.

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