Global Asymptotic Behavior of a Two-dimensional System of Difference Equations Modeling Cooperation

2003 ◽  
Vol 9 (1) ◽  
pp. 149-159 ◽  
Author(s):  
M.R.S. Kulenović ◽  
M. Nurkanović
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Dimensional System ◽  
Two Dimensional ◽  
System Of Difference Equations ◽  
Two Dimensional System

scholarly journals On the Global Asymptotic Stability of A Two Dimensional System of Difference Equations with Quadratic Terms

2020 ◽  
Author(s):  
Erkan Taşdemir
Keyword(s):  
Asymptotic Stability ◽  
Rate Of Convergence ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Dimensional System ◽  
Two Dimensional ◽  
System Of Difference Equations ◽  
Related System ◽  
Initial Values ◽  
Two Dimensional System

In this paper, we study the global asymptotically stability of following system of difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-1}²)),y_{n+1}=A+B((x_{n})/(x_{n-1}²)) where A and B are positive numbers and the initial values are positive numbers. We also investigate the rate of convergence and oscillation behaviour of the solutions of related system.

scholarly journals Oscillatory criteria for two-dimensional system of difference equations

2011 ◽  
Vol 48 (1) ◽  
pp. 153-163
Author(s):  
Zdeněk Opluštil
Keyword(s):  
Difference Equations ◽  
Dimensional System ◽  
Two Dimensional ◽  
Linear Difference Equations ◽  
System Of Difference Equations ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
Two Dimensional System

Abstract Some oscillation criteria are established for two-dimensional systems of first order linear difference equations.

scholarly journals On a solvable three-dimensional system of difference equations

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1167-1186
Author(s):  
Merve Kara ◽  
Yasin Yazlik
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Three Dimensional ◽  
Asymptotic Behavior Of Solutions ◽  
Dimensional System ◽  
Real Numbers ◽  
System Of Difference Equations ◽  
Initial Values ◽  
Forbidden Set ◽  
Three Dimensional System

In this paper, we show that the following three-dimensional system of difference equations xn = zn-2xn-3/axn-3 + byn-1, yn = xn-2yn-3/cyn-3 + dzn-1, zn = yn-2zn-3/ezn-3+ fxn-1, n ? N0, where the parameters a, b, c, d, e, f and the initial values x-i, y-i, z-i, i ? {1, 2, 3}, are real numbers, can be solved, extending further some results in literature. Also, we determine the asymptotic behavior of solutions and the forbidden set of the initial values by using the obtained formulas.

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