Dynamical properties of some rational systems of difference equations

2020 ◽  
Author(s):  
A. Q. Khan ◽  
S. M. Qureshi
Keyword(s):  
Difference Equations ◽  
Dynamical Properties ◽  
Rational Systems

scholarly journals On some rational systems of difference equations

2017 ◽  
Vol 11 (01) ◽  
pp. 49-72 ◽  
Author(s):  
M. M. El-Dessoky ◽  
A. Khaliq ◽  
A. Asiri
Keyword(s):  
Difference Equations ◽  
Rational Systems

Dynamics and Behaviour of Some Rational Systems of Difference Equations

2016 ◽  
Vol 13 (11) ◽  
pp. 8583-8599 ◽  
Author(s):  
Faris Alzahrani ◽  
Abdul Khaliq ◽  
E. M Elsayed
Keyword(s):  
Difference Equations ◽  
Rational Systems

scholarly journals Global Dynamics of a 3 × 6 System of Difference Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
S. M. Qureshi ◽  
A. Q. Khan
Keyword(s):  
Difference Equations ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
System Of Difference Equations ◽  
Globally Asymptotically Stable ◽  
Rational Difference Equations ◽  
Dynamical Properties ◽  
Theoretical Results

In the proposed work, global dynamics of a 3×6 system of rational difference equations has been studied in the interior of R+3. It is proved that system has at least one and at most seven boundary equilibria and a unique +ve equilibrium under certain parametric conditions. By utilizing method of Linearization, local dynamical properties about equilibria have been investigated. It is shown that every +ve solution of the system is bounded, and equilibrium P0 becomes a globally asymptotically stable if α1<α2,α4<α5, α7<α8. It is also shown that every +ve solution of the system converges to P0. Finally theoretical results are verified numerically.

On a Third Order Rational Systems of Difference Equations

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
N. Touafek ◽  
E.M. Elsayed
Keyword(s):  
Difference Equations ◽  
Initial Conditions ◽  
Real Numbers ◽  
Third Order ◽  
Rational Systems

Abstract In this paper we investigate the form of the solutions of the following systems of difference equations of order three with a nonzero real numbers initial conditions.

scholarly journals Global Behavior of Four Competitive Rational Systems of Difference Equations in the Plane

2009 ◽  
Vol 2009 ◽  
pp. 1-34 ◽  
Author(s):  
M. Garić-Demirović ◽  
M. R. S. Kulenović ◽  
M. Nurkanović
Keyword(s):  
Difference Equations ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Saddle Points ◽  
Global Behavior ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Rational Systems ◽  
Global Stable Manifolds ◽  
Basins Of Attractions

We investigate the global dynamics of solutions of four distinct competitive rational systems of difference equations in the plane. We show that the basins of attractions of different locally asymptotically stable equilibrium points are separated by the global stable manifolds of either saddle points or nonhyperbolic equilibrium points. Our results give complete answer to Open Problem 2 posed recently by Camouzis et al. (2009).

Dynamical properties of a class of higher-order nonlinear difference equations

2011 ◽  
Vol 217 (12) ◽  
pp. 5476-5479 ◽  
Author(s):  
Maoxin Liao ◽  
Xianhua Tang ◽  
Zigen Ouyang ◽  
Changjin Xu
Keyword(s):  
Difference Equations ◽  
Higher Order ◽  
Nonlinear Difference Equations ◽  
Dynamical Properties
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