Global behavior of a max-type system of difference equations with four variables

2021 ◽  
Author(s):  
Taixiang Sun ◽  
Guangwang Su ◽  
Caihong Han ◽  
Lue Li ◽  
Weizhen Quan
Keyword(s):  
Difference Equations ◽  
Type System ◽  
Global Behavior ◽  
System Of Difference Equations

scholarly journals Solution of the Maximum of Difference Equation xn+1=max{Axn−1,ynxn};yn+1=max{Ayn−1,xnyn}\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\}}}

2020 ◽  
Vol 5 (1) ◽  
pp. 275-282
Author(s):  
Dagistan Simsek ◽  
Burak Ogul ◽  
Fahreddin Abdullayev
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Initial Conditions ◽  
Type System ◽  
Global Behavior ◽  
System Of Difference Equations

AbstractIn the recent years, there has been a lot of interest in studying the global behavior of, the socalled, max-type difference equations; see, for example, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. The study of max type difference equations has also attracted some attention recently. We study the behaviour of the solutions of the following system of difference equation with the max operator: paper deals with the behaviour of the solutions of the max type system of difference equations, (1)\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\},}} where the parametr A and initial conditions x−1,x0, y−1,y0 are positive reel numbers.

Solvability of a product-type system of difference equations with six parameters

2016 ◽  
Vol 8 (1) ◽  
pp. 29-51 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Closed Form ◽  
Difference Equations ◽  
Type System ◽  
Product Type ◽  
System Of Difference Equations ◽  
Initial Values ◽  
Complex Valued

AbstractClosed form formulas for well-defined complex-valued solutions to a product-type system of difference equations of interest with six parameters are presented. The form of the solutions is described in detail in terms of the parameters and initial values.

scholarly journals Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Guangwang Su ◽  
Taixiang Sun ◽  
Bin Qin
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Initial Conditions ◽  
Type System ◽  
Higher Order ◽  
System Of Difference Equations

We study in this paper the following max-type system of difference equations of higher order: xn=max{A,yn-k/xn-1} and yn=max{B,xn-k/yn-1}, n∈{0,1,2,…}, where A≥B>0, k≥1, and the initial conditions x-k,y-k,x-k+1,y-k+1,…,x-1,y-1∈(0,+∞). We show that (1) if AB>1, then every solution of the above system is periodic with period 2 eventually. (2) If AB=1>B, then every solution of the above system is periodic with period 2k or 2 eventually. (3) If A=B=1 or AB<1, then the above system has a solution which is not periodic eventually.

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