On the solutions of a max-type system of difference equations with period-two parameters

Su, Guangwang; Sun, Taixiang; Qin, Bin

doi:10.1186/s13662-018-1826-1

Cited by 6 publications

(3 citation statements)

References 27 publications

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“…In [25], Su et al, inspired by above results of (1.4), investigated the periodicity of positive solutions of the following max-type systems of difference equations…”

Section: Introductionmentioning

confidence: 99%

Eventual periodicity of a max-type system of difference equations of higher order with four variables

Su¹,

Sun²,

Han³

et al. 2022

MMN

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The aim of this paper is to investigate eventual periodicity of the following max-type system of difference equations of higher order with four variableswhere k is a positive integer, A, B,C, D ∈ (0, +∞) with A ≤ B and C ≤ D, and the initial valuesn=−k of this system which is not eventually periodic.(2) If BD = AC = 1 with A ̸ = C or BD > AC = 1 or AC > 1, then every solution of this system is eventually periodic.

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“…In [25], Su et al, inspired by above results of (1.4), investigated the periodicity of positive solutions of the following max-type systems of difference equations…”

Section: Introductionmentioning

confidence: 99%

Eventual periodicity of a max-type system of difference equations of higher order with four variables

Su¹,

Sun²,

Han³

et al. 2022

MMN

View full text Add to dashboard Cite

show abstract

“…e study of the system of max-type di erence equations attracted recently a considerable attention; see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], and the references listed therein. is type of difference equations stemming from, for example, certain models are useful in automatic control theory (see [27]).…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of Three-Dimensional Max-Type System of Difference Equations

Khaliq

Sadiq

Khan

et al. 2022

Mathematical Problems in Engineering

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In this paper, we deal with the form and the periodicity of the solutions of the max-type system of difference equations u n + 1 = max A n / v n − 1 , u n − 1 , v n + 1 = max B n / w n − 1 , w n + 1 = max C n / u n − 1 , w n − 1 where the initial conditions u − 1 , u 0 ∈ 0 , ∞ , v − 1 , v 0 ∈ 0 , ∞ , w − 1 , w 0 ∈ 0 , ∞ and A n n ∈ N 0 , B n n ∈ N 0 , C n n ∈ N 0 are positive two-periodic sequences.

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“…with A, B ∈ R + and showed that every positive solution of the above system is eventually periodic. Further, Su et al [18] studied eventual periodicity of the following max-type system of difference equations:…”

Section: Introductionmentioning

confidence: 99%

Eventual periodicity of the fuzzy max-difference equation $x_{n} = \max \{ C, \frac{x_{n-m-k}}{x_{n-m}}\}$

Han

et al. 2020

Adv Differ Equ

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In this paper, we study the eventual periodicity of the fuzzy max-type difference equation $x_{n} =\max \{C , \frac{x_{n-m-k}}{x_{n-m} }\}, n\in \{0,1,\ldots \} $ x n = max { C , x n − m − k x n − m } , n ∈ { 0 , 1 , … } , where m and k are positive integers, C and the initial values are positive fuzzy numbers. Let the support $\operatorname{supp} C=\overline{\{t : C(t) > 0\}}=[C_{1},C_{2}]$ supp C = { t : C ( t ) > 0 } ‾ = [ C 1 , C 2 ] of C. We show that: (1) if $C_{1}>1$ C 1 > 1 , then every positive solution of this equation equals C eventually; (2) there exists a positive fuzzy number C with $C_{1}=1$ C 1 = 1 such that this equation has a positive solution which is not eventually periodic; (3) if $C_{2}\leq 1$ C 2 ≤ 1 , then this equation has a positive solution which is not eventually periodic; (4) if $C_{1}<1<C_{2}$ C 1 < 1 < C 2 , then every positive solution of the above equation is not eventually periodic.

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On the solutions of a max-type system of difference equations with period-two parameters

Abstract: In this paper, we study the following max-type system of difference equations:where A n , B n ∈ (0, +∞) are periodic sequences with period 2 and the initial values x -1 , y -1 , x -2 , y -2 ∈ (0, +∞). We show that every solution of the above system is eventually periodic.

Cited by 6 publications

References 27 publications

Eventual periodicity of a max-type system of difference equations of higher order with four variables

Eventual periodicity of a max-type system of difference equations of higher order with four variables

Exact Solutions of Three-Dimensional Max-Type System of Difference Equations

Eventual periodicity of the fuzzy max-difference equation $x_{n} = \max \{ C, \frac{x_{n-m-k}}{x_{n-m}}\}$

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