scholarly journals Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations

2009 ◽  
Vol 2009 (1) ◽  
pp. 128602 ◽  
Author(s):  
Sukanya Basu ◽  
Orlando Merino
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Global Behavior ◽  
Rational Difference Equations

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)).

Global behavior of two third order rational difference equations with quadratic terms

2019 ◽  
Vol 69 (1) ◽  
pp. 147-158 ◽  
Author(s):  
R. Abo-Zeid
Keyword(s):  
Explicit Formula ◽  
Difference Equations ◽  
Initial Conditions ◽  
Global Behavior ◽  
Real Numbers ◽  
Positive Real ◽  
Third Order ◽  
Rational Difference Equations ◽  
The Difference

Abstract In this paper, we determine the forbidden sets, introduce an explicit formula for the solutions and discuss the global behaviors of solutions of the difference equations $$\begin{array}{} \displaystyle x_{n+1}=\frac{ax_{n}x_{n-1}}{bx_{n-1}+ cx_{n-2}},\quad n=0,1,\ldots \end{array} $$ where a,b,c are positive real numbers and the initial conditions x−2,x−1,x0 are real numbers.

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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