scholarly journals On a close to symmetric system of difference equations of second order

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Stevo Stević ◽  
Bratislav Iričanin ◽  
Zdeněk Šmarda
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Symmetric System ◽  
System Of Difference Equations

scholarly journals On the Global Asymptotic Stability of a Second-Order System of Difference Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Ibrahim Yalcinkaya
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Second Order ◽  
Order System ◽  
Sufficient Condition ◽  
System Of Difference Equations ◽  
Initial Values

A sufficient condition is obtained for the global asymptotic stability of the following system of difference equations where the parameter and the initial values (for .

scholarly journals Periodic Solutions for a System of Difference Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Shugui Kang ◽  
Bao Shi
Keyword(s):  
Nonlinear Systems ◽  
Critical Point ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Second Order ◽  
System Of Difference Equations

This paper deals with the second-order nonlinear systems of difference equations, we obtain the existence theorems of periodic solutions. The theorems are proved by using critical point theory.

scholarly journals Characterization of Homogeneous System of Difference Equations

2021 ◽  
Vol 32 (1) ◽  
pp. 25
Author(s):  
Huda Hussein Abed ◽  
Bassam Jabbar Al-Asadi
Keyword(s):  
Difference Equations ◽  
Homogeneous System ◽  
Second Order ◽  
System Of Difference Equations ◽  
The Matrix

In this paper, we introduced new definitions of the system of homogenous difference equations of order two; namely homogenous and semi homogenous system, where we focused on finding the equivalents for these definitions of order one as well as of order greater than one for the system of difference equations of the second order and given some examples. We also a given formula to find the power of the matrix that we used in this research.

scholarly journals Neimark-Sacker, flip and transcritical bifurcation in a symmetric system of difference equations with exponential terms

2021 ◽  
Author(s):  
Chrysoula Mylona ◽  
Garyfalos Papaschinopoulos ◽  
Christos Schinas
Keyword(s):  
Normal Form ◽  
Difference Equations ◽  
Bifurcation Analysis ◽  
Center Manifold ◽  
Transcritical Bifurcation ◽  
Symmetric System ◽  
Center Manifold Theory ◽  
Real Numbers ◽  
System Of Difference Equations ◽  
Manifold Theory

In this paper, we study the conditions under which the following symmetric system of difference equations with exponential terms: \[ x_{n+1} =a_1\frac{y_n}{b_1+y_n} +c_1\frac{x_ne^{k_1-d_1x_n}}{1+e^{k_1-d_1x_n}},\] \[ y_{n+1} =a_2\frac{x_n}{b_2+x_n} +c_2\frac{y_ne^{k_2-d_2y_n}}{1+e^{k_2-d_2y_n}}\] where $a_i$, $b_i$, $c_i$, $d_i$, $k_i$, for $i=1,2$, are real constants and the initial values $x_0$, $y_0$ are real numbers, undergoes Neimark-Sacker, flip and transcritical bifurcation. The analysis is conducted applying center manifold theory and the normal form bifurcation analysis.

On a nonlinear second order system of difference equations

2013 ◽  
Vol 219 (24) ◽  
pp. 11388-11394 ◽  
Author(s):  
Stevo Stević ◽  
Mohammed A. Alghamdi ◽  
Abdullah Alotaibi ◽  
Naseer Shahzad
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Order System ◽  
System Of Difference Equations
Sign in / Sign up

Export Citation Format

Share Document