scholarly journals Global Dynamics, Boundedness, and Semicycle Analysis of a Difference Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Abdul Qadeer Khan ◽  
Hamdy El-Metwally
Keyword(s):  
Difference Equation ◽  
Local Stability ◽  
Second Order ◽  
Nonlinear Difference Equation ◽  
Global Dynamics

In this paper, we explore local stability, attractor, periodicity character, and boundedness solutions of the second-order nonlinear difference equation. Finally, obtained results are verified numerically.

scholarly journals GLOBAL STABILITY OF SECOND ORDER NONLINEAR DIFFERENCE EQUATION

2021 ◽  
Vol 23 (2) ◽  
pp. 201-223
Author(s):  
Hanan S. Gafel
Keyword(s):  
Difference Equation ◽  
Global Stability ◽  
Second Order ◽  
Nonlinear Difference Equation

scholarly journals Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Senada Kalabušić ◽  
M. R. S. Kulenović ◽  
M. Mehuljić
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Global Asymptotic Stability ◽  
Local Stability ◽  
Initial Conditions ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Global Dynamics ◽  
Second Order Difference Equation ◽  
The Difference

We investigate the local stability and the global asymptotic stability of the difference equationxn+1=αxn2+βxnxn-1+γxn-1/Axn2+Bxnxn-1+Cxn-1,n=0,1,…with nonnegative parameters and initial conditions such thatAxn2+Bxnxn-1+Cxn-1>0, for alln≥0. We obtain the local stability of the equilibrium for all values of parameters and give some global asymptotic stability results for some values of the parameters. We also obtain global dynamics in the special case, whereβ=B=0, in which case we show that such equation exhibits a global period doubling bifurcation.

scholarly journals Monotonicity of Eventually Positive Solutions for a Second Order Nonlinear Difference Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Huiqin Chen ◽  
Zhen Jin ◽  
Shugui Kang
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Difference Equation ◽  
Monotone Solutions

We derive several sufficient conditions for monotonicity of eventually positive solutions on a class of second order perturbed nonlinear difference equation. Furthermore, we obtain a few nonexistence criteria for eventually positive monotone solutions of this equation. Examples are provided to illustrate our main results.

scholarly journals Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-17
Author(s):  
Xiu-Mei Jia ◽  
Wan-Tong Li
Keyword(s):  
Difference Equation ◽  
Global Attractor ◽  
Positive Solutions ◽  
Local Stability ◽  
Global Attractivity ◽  
Initial Conditions ◽  
Higher Order ◽  
Nonlinear Difference Equation ◽  
Positive Equilibrium ◽  
Prime Period

We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: , , where the parameters and the initial conditions . We show that the unique positive equilibrium of this equation is a global attractor under certain conditions.

scholarly journals Oscillation of Second Order Nonlinear Difference Equation with Continuous Variable

2001 ◽  
Vol 255 (1) ◽  
pp. 349-357 ◽  
Author(s):  
Zhenguo Zhang ◽  
Ping Bi ◽  
Jianfeng Chen
Keyword(s):  
Difference Equation ◽  
Continuous Variable ◽  
Second Order ◽  
Nonlinear Difference Equation

Global dynamics of quadratic second order difference equation in the first quadrant

2014 ◽  
Vol 227 ◽  
pp. 50-65 ◽  
Author(s):  
J. Bektešević ◽  
M.R.S. Kulenović ◽  
E. Pilav
Keyword(s):  
Difference Equation ◽  
Second Order ◽  
Global Dynamics ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

scholarly journals Global behaviour of a second-order nonlinear difference equation

2011 ◽  
Vol 17 (10) ◽  
pp. 1471-1486 ◽  
Author(s):  
Ignacio Bajo ◽  
Eduardo Liz
Keyword(s):  
Difference Equation ◽  
Second Order ◽  
Nonlinear Difference Equation ◽  
Global Behaviour

scholarly journals On a class of second-order nonlinear difference equation

2011 ◽  
Vol 2011 (1) ◽  
pp. 46 ◽  
Author(s):  
Li Dongsheng ◽  
Zou Shuliang ◽  
Liao Maoxin
Keyword(s):  
Difference Equation ◽  
Second Order ◽  
Nonlinear Difference Equation

scholarly journals Local Stability of Period Two Cycles of Second Order Rational Difference Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
S. Atawna ◽  
R. Abu-Saris ◽  
I. Hashim
Keyword(s):  
Difference Equation ◽  
Local Stability ◽  
Second Order ◽  
Rational Difference Equation
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