On periodic solutions of a class of k-dimensional systems of max-type difference equations
Some sufficient conditions are given such that the following system of difference equations: x ( 1 ) ( n + 1 ) = max 1 ≤ j ≤ l 1 { f 1 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , x ( 2 ) ( n + 1 ) = max 1 ≤ j ≤ l 2 { f 2 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , ⋮ x ( k ) ( n + 1 ) = max 1...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Stević, Stevo [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Rechteinformationen: |
Nutzungsrecht: © The Author(s) 2016 |
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| Schlagwörter: |
Difference and Functional Equations Partial Differential Equations max-type system of difference equations Ordinary Differential Equations |
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| Übergeordnetes Werk: |
Enthalten in: Advances in difference equations - [Sylvania, Ohio] : Hindawi Publ. Corp., 2004, 2016(2016), 1, Seite 1-10 |
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| Übergeordnetes Werk: |
volume:2016 ; year:2016 ; number:1 ; pages:1-10 |
| Links: |
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| DOI / URN: |
10.1186/s13662-016-0977-1 |
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| Katalog-ID: |
OLC1986370593 |
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| 520 | |a Some sufficient conditions are given such that the following system of difference equations: x ( 1 ) ( n + 1 ) = max 1 ≤ j ≤ l 1 { f 1 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , x ( 2 ) ( n + 1 ) = max 1 ≤ j ≤ l 2 { f 2 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , ⋮ x ( k ) ( n + 1 ) = max 1 ≤ j ≤ l k { f k j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , $$\begin{aligned} &x^{(1)}(n+1)=\max_{1\le j\le l_{1}} \bigl\{ f_{1j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &x^{(2)}(n+1)=\max_{1\le j\le l_{2}} \bigl\{ f_{2j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &\vdots \\ &x^{(k)}(n+1)=\max_{1\le j\le l_{k}} \bigl\{ f_{kj} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \end{aligned}$$ n ∈ N 0 $n\in {\mathbb {N}}_{0}$ , where k ∈ N $k\in {\mathbb {N}}$ , l i ∈ N $l_{i}\in {\mathbb {N}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , x ( i ) ( 0 ) ∈ R $x^{(i)}(0)\in {\mathbb {R}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , has a unique periodic solution attracting all the solutions to the system. Our main result considerably generalizes some recent results in the literature and simplifies their proofs. | ||
| 540 | |a Nutzungsrecht: © The Author(s) 2016 | ||
| 650 | 4 | |a Difference and Functional Equations | |
| 650 | 4 | |a Partial Differential Equations | |
| 650 | 4 | |a max-type system of difference equations | |
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| 650 | 4 | |a existence of periodic solutions | |
| 650 | 4 | |a Functional Analysis | |
| 650 | 4 | |a 39A23 | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a global attractivity | |
| 650 | 4 | |a Mathematics | |
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10.1186/s13662-016-0977-1 doi PQ20161201 (DE-627)OLC1986370593 (DE-599)GBVOLC1986370593 (PRQ)c1617-fdcb932a0cf1ff96ffae5318f9438e4b8666cb0407e1b7593dcf807d336565dd3 (KEY)0544041620160000016000100001onperiodicsolutionsofaclassofkdimensionalsystemsof DE-627 ger DE-627 rakwb eng 510 ZDB 31.49 bkl Stević, Stevo verfasserin aut On periodic solutions of a class of k-dimensional systems of max-type difference equations 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Some sufficient conditions are given such that the following system of difference equations: x ( 1 ) ( n + 1 ) = max 1 ≤ j ≤ l 1 { f 1 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , x ( 2 ) ( n + 1 ) = max 1 ≤ j ≤ l 2 { f 2 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , ⋮ x ( k ) ( n + 1 ) = max 1 ≤ j ≤ l k { f k j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , $$\begin{aligned} &x^{(1)}(n+1)=\max_{1\le j\le l_{1}} \bigl\{ f_{1j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &x^{(2)}(n+1)=\max_{1\le j\le l_{2}} \bigl\{ f_{2j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &\vdots \\ &x^{(k)}(n+1)=\max_{1\le j\le l_{k}} \bigl\{ f_{kj} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \end{aligned}$$ n ∈ N 0 $n\in {\mathbb {N}}_{0}$ , where k ∈ N $k\in {\mathbb {N}}$ , l i ∈ N $l_{i}\in {\mathbb {N}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , x ( i ) ( 0 ) ∈ R $x^{(i)}(0)\in {\mathbb {R}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , has a unique periodic solution attracting all the solutions to the system. Our main result considerably generalizes some recent results in the literature and simplifies their proofs. Nutzungsrecht: © The Author(s) 2016 Difference and Functional Equations Partial Differential Equations max-type system of difference equations Ordinary Differential Equations Analysis existence of periodic solutions Functional Analysis 39A23 Mathematics, general global attractivity Mathematics Enthalten in Advances in difference equations [Sylvania, Ohio] : Hindawi Publ. Corp., 2004 2016(2016), 1, Seite 1-10 (DE-627)394569423 (DE-600)2161260-2 (DE-576)9394569421 1687-1839 nnns volume:2016 year:2016 number:1 pages:1-10 http://dx.doi.org/10.1186/s13662-016-0977-1 Volltext http://search.proquest.com/docview/1824487480 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4310 31.49 AVZ AR 2016 2016 1 1-10 |
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10.1186/s13662-016-0977-1 doi PQ20161201 (DE-627)OLC1986370593 (DE-599)GBVOLC1986370593 (PRQ)c1617-fdcb932a0cf1ff96ffae5318f9438e4b8666cb0407e1b7593dcf807d336565dd3 (KEY)0544041620160000016000100001onperiodicsolutionsofaclassofkdimensionalsystemsof DE-627 ger DE-627 rakwb eng 510 ZDB 31.49 bkl Stević, Stevo verfasserin aut On periodic solutions of a class of k-dimensional systems of max-type difference equations 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Some sufficient conditions are given such that the following system of difference equations: x ( 1 ) ( n + 1 ) = max 1 ≤ j ≤ l 1 { f 1 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , x ( 2 ) ( n + 1 ) = max 1 ≤ j ≤ l 2 { f 2 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , ⋮ x ( k ) ( n + 1 ) = max 1 ≤ j ≤ l k { f k j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , $$\begin{aligned} &x^{(1)}(n+1)=\max_{1\le j\le l_{1}} \bigl\{ f_{1j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &x^{(2)}(n+1)=\max_{1\le j\le l_{2}} \bigl\{ f_{2j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &\vdots \\ &x^{(k)}(n+1)=\max_{1\le j\le l_{k}} \bigl\{ f_{kj} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \end{aligned}$$ n ∈ N 0 $n\in {\mathbb {N}}_{0}$ , where k ∈ N $k\in {\mathbb {N}}$ , l i ∈ N $l_{i}\in {\mathbb {N}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , x ( i ) ( 0 ) ∈ R $x^{(i)}(0)\in {\mathbb {R}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , has a unique periodic solution attracting all the solutions to the system. Our main result considerably generalizes some recent results in the literature and simplifies their proofs. Nutzungsrecht: © The Author(s) 2016 Difference and Functional Equations Partial Differential Equations max-type system of difference equations Ordinary Differential Equations Analysis existence of periodic solutions Functional Analysis 39A23 Mathematics, general global attractivity Mathematics Enthalten in Advances in difference equations [Sylvania, Ohio] : Hindawi Publ. Corp., 2004 2016(2016), 1, Seite 1-10 (DE-627)394569423 (DE-600)2161260-2 (DE-576)9394569421 1687-1839 nnns volume:2016 year:2016 number:1 pages:1-10 http://dx.doi.org/10.1186/s13662-016-0977-1 Volltext http://search.proquest.com/docview/1824487480 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4310 31.49 AVZ AR 2016 2016 1 1-10 |
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10.1186/s13662-016-0977-1 doi PQ20161201 (DE-627)OLC1986370593 (DE-599)GBVOLC1986370593 (PRQ)c1617-fdcb932a0cf1ff96ffae5318f9438e4b8666cb0407e1b7593dcf807d336565dd3 (KEY)0544041620160000016000100001onperiodicsolutionsofaclassofkdimensionalsystemsof DE-627 ger DE-627 rakwb eng 510 ZDB 31.49 bkl Stević, Stevo verfasserin aut On periodic solutions of a class of k-dimensional systems of max-type difference equations 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Some sufficient conditions are given such that the following system of difference equations: x ( 1 ) ( n + 1 ) = max 1 ≤ j ≤ l 1 { f 1 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , x ( 2 ) ( n + 1 ) = max 1 ≤ j ≤ l 2 { f 2 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , ⋮ x ( k ) ( n + 1 ) = max 1 ≤ j ≤ l k { f k j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , $$\begin{aligned} &x^{(1)}(n+1)=\max_{1\le j\le l_{1}} \bigl\{ f_{1j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &x^{(2)}(n+1)=\max_{1\le j\le l_{2}} \bigl\{ f_{2j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &\vdots \\ &x^{(k)}(n+1)=\max_{1\le j\le l_{k}} \bigl\{ f_{kj} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \end{aligned}$$ n ∈ N 0 $n\in {\mathbb {N}}_{0}$ , where k ∈ N $k\in {\mathbb {N}}$ , l i ∈ N $l_{i}\in {\mathbb {N}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , x ( i ) ( 0 ) ∈ R $x^{(i)}(0)\in {\mathbb {R}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , has a unique periodic solution attracting all the solutions to the system. Our main result considerably generalizes some recent results in the literature and simplifies their proofs. Nutzungsrecht: © The Author(s) 2016 Difference and Functional Equations Partial Differential Equations max-type system of difference equations Ordinary Differential Equations Analysis existence of periodic solutions Functional Analysis 39A23 Mathematics, general global attractivity Mathematics Enthalten in Advances in difference equations [Sylvania, Ohio] : Hindawi Publ. Corp., 2004 2016(2016), 1, Seite 1-10 (DE-627)394569423 (DE-600)2161260-2 (DE-576)9394569421 1687-1839 nnns volume:2016 year:2016 number:1 pages:1-10 http://dx.doi.org/10.1186/s13662-016-0977-1 Volltext http://search.proquest.com/docview/1824487480 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4310 31.49 AVZ AR 2016 2016 1 1-10 |
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10.1186/s13662-016-0977-1 doi PQ20161201 (DE-627)OLC1986370593 (DE-599)GBVOLC1986370593 (PRQ)c1617-fdcb932a0cf1ff96ffae5318f9438e4b8666cb0407e1b7593dcf807d336565dd3 (KEY)0544041620160000016000100001onperiodicsolutionsofaclassofkdimensionalsystemsof DE-627 ger DE-627 rakwb eng 510 ZDB 31.49 bkl Stević, Stevo verfasserin aut On periodic solutions of a class of k-dimensional systems of max-type difference equations 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Some sufficient conditions are given such that the following system of difference equations: x ( 1 ) ( n + 1 ) = max 1 ≤ j ≤ l 1 { f 1 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , x ( 2 ) ( n + 1 ) = max 1 ≤ j ≤ l 2 { f 2 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , ⋮ x ( k ) ( n + 1 ) = max 1 ≤ j ≤ l k { f k j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , $$\begin{aligned} &x^{(1)}(n+1)=\max_{1\le j\le l_{1}} \bigl\{ f_{1j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &x^{(2)}(n+1)=\max_{1\le j\le l_{2}} \bigl\{ f_{2j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &\vdots \\ &x^{(k)}(n+1)=\max_{1\le j\le l_{k}} \bigl\{ f_{kj} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \end{aligned}$$ n ∈ N 0 $n\in {\mathbb {N}}_{0}$ , where k ∈ N $k\in {\mathbb {N}}$ , l i ∈ N $l_{i}\in {\mathbb {N}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , x ( i ) ( 0 ) ∈ R $x^{(i)}(0)\in {\mathbb {R}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , has a unique periodic solution attracting all the solutions to the system. Our main result considerably generalizes some recent results in the literature and simplifies their proofs. Nutzungsrecht: © The Author(s) 2016 Difference and Functional Equations Partial Differential Equations max-type system of difference equations Ordinary Differential Equations Analysis existence of periodic solutions Functional Analysis 39A23 Mathematics, general global attractivity Mathematics Enthalten in Advances in difference equations [Sylvania, Ohio] : Hindawi Publ. Corp., 2004 2016(2016), 1, Seite 1-10 (DE-627)394569423 (DE-600)2161260-2 (DE-576)9394569421 1687-1839 nnns volume:2016 year:2016 number:1 pages:1-10 http://dx.doi.org/10.1186/s13662-016-0977-1 Volltext http://search.proquest.com/docview/1824487480 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4310 31.49 AVZ AR 2016 2016 1 1-10 |
| allfieldsSound |
10.1186/s13662-016-0977-1 doi PQ20161201 (DE-627)OLC1986370593 (DE-599)GBVOLC1986370593 (PRQ)c1617-fdcb932a0cf1ff96ffae5318f9438e4b8666cb0407e1b7593dcf807d336565dd3 (KEY)0544041620160000016000100001onperiodicsolutionsofaclassofkdimensionalsystemsof DE-627 ger DE-627 rakwb eng 510 ZDB 31.49 bkl Stević, Stevo verfasserin aut On periodic solutions of a class of k-dimensional systems of max-type difference equations 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Some sufficient conditions are given such that the following system of difference equations: x ( 1 ) ( n + 1 ) = max 1 ≤ j ≤ l 1 { f 1 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , x ( 2 ) ( n + 1 ) = max 1 ≤ j ≤ l 2 { f 2 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , ⋮ x ( k ) ( n + 1 ) = max 1 ≤ j ≤ l k { f k j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , $$\begin{aligned} &x^{(1)}(n+1)=\max_{1\le j\le l_{1}} \bigl\{ f_{1j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &x^{(2)}(n+1)=\max_{1\le j\le l_{2}} \bigl\{ f_{2j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &\vdots \\ &x^{(k)}(n+1)=\max_{1\le j\le l_{k}} \bigl\{ f_{kj} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \end{aligned}$$ n ∈ N 0 $n\in {\mathbb {N}}_{0}$ , where k ∈ N $k\in {\mathbb {N}}$ , l i ∈ N $l_{i}\in {\mathbb {N}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , x ( i ) ( 0 ) ∈ R $x^{(i)}(0)\in {\mathbb {R}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , has a unique periodic solution attracting all the solutions to the system. Our main result considerably generalizes some recent results in the literature and simplifies their proofs. Nutzungsrecht: © The Author(s) 2016 Difference and Functional Equations Partial Differential Equations max-type system of difference equations Ordinary Differential Equations Analysis existence of periodic solutions Functional Analysis 39A23 Mathematics, general global attractivity Mathematics Enthalten in Advances in difference equations [Sylvania, Ohio] : Hindawi Publ. Corp., 2004 2016(2016), 1, Seite 1-10 (DE-627)394569423 (DE-600)2161260-2 (DE-576)9394569421 1687-1839 nnns volume:2016 year:2016 number:1 pages:1-10 http://dx.doi.org/10.1186/s13662-016-0977-1 Volltext http://search.proquest.com/docview/1824487480 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4310 31.49 AVZ AR 2016 2016 1 1-10 |
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Stević, Stevo ddc 510 bkl 31.49 misc Difference and Functional Equations misc Partial Differential Equations misc max-type system of difference equations misc Ordinary Differential Equations misc Analysis misc existence of periodic solutions misc Functional Analysis misc 39A23 misc Mathematics, general misc global attractivity misc Mathematics On periodic solutions of a class of k-dimensional systems of max-type difference equations |
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510 ZDB 31.49 bkl On periodic solutions of a class of k-dimensional systems of max-type difference equations Difference and Functional Equations Partial Differential Equations max-type system of difference equations Ordinary Differential Equations Analysis existence of periodic solutions Functional Analysis 39A23 Mathematics, general global attractivity Mathematics |
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on periodic solutions of a class of k-dimensional systems of max-type difference equations |
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On periodic solutions of a class of k-dimensional systems of max-type difference equations |
| abstract |
Some sufficient conditions are given such that the following system of difference equations: x ( 1 ) ( n + 1 ) = max 1 ≤ j ≤ l 1 { f 1 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , x ( 2 ) ( n + 1 ) = max 1 ≤ j ≤ l 2 { f 2 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , ⋮ x ( k ) ( n + 1 ) = max 1 ≤ j ≤ l k { f k j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , $$\begin{aligned} &x^{(1)}(n+1)=\max_{1\le j\le l_{1}} \bigl\{ f_{1j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &x^{(2)}(n+1)=\max_{1\le j\le l_{2}} \bigl\{ f_{2j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &\vdots \\ &x^{(k)}(n+1)=\max_{1\le j\le l_{k}} \bigl\{ f_{kj} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \end{aligned}$$ n ∈ N 0 $n\in {\mathbb {N}}_{0}$ , where k ∈ N $k\in {\mathbb {N}}$ , l i ∈ N $l_{i}\in {\mathbb {N}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , x ( i ) ( 0 ) ∈ R $x^{(i)}(0)\in {\mathbb {R}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , has a unique periodic solution attracting all the solutions to the system. Our main result considerably generalizes some recent results in the literature and simplifies their proofs. |
| abstractGer |
Some sufficient conditions are given such that the following system of difference equations: x ( 1 ) ( n + 1 ) = max 1 ≤ j ≤ l 1 { f 1 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , x ( 2 ) ( n + 1 ) = max 1 ≤ j ≤ l 2 { f 2 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , ⋮ x ( k ) ( n + 1 ) = max 1 ≤ j ≤ l k { f k j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , $$\begin{aligned} &x^{(1)}(n+1)=\max_{1\le j\le l_{1}} \bigl\{ f_{1j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &x^{(2)}(n+1)=\max_{1\le j\le l_{2}} \bigl\{ f_{2j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &\vdots \\ &x^{(k)}(n+1)=\max_{1\le j\le l_{k}} \bigl\{ f_{kj} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \end{aligned}$$ n ∈ N 0 $n\in {\mathbb {N}}_{0}$ , where k ∈ N $k\in {\mathbb {N}}$ , l i ∈ N $l_{i}\in {\mathbb {N}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , x ( i ) ( 0 ) ∈ R $x^{(i)}(0)\in {\mathbb {R}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , has a unique periodic solution attracting all the solutions to the system. Our main result considerably generalizes some recent results in the literature and simplifies their proofs. |
| abstract_unstemmed |
Some sufficient conditions are given such that the following system of difference equations: x ( 1 ) ( n + 1 ) = max 1 ≤ j ≤ l 1 { f 1 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , x ( 2 ) ( n + 1 ) = max 1 ≤ j ≤ l 2 { f 2 j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , ⋮ x ( k ) ( n + 1 ) = max 1 ≤ j ≤ l k { f k j ( n , x ( 1 ) ( n ) , … , x ( k ) ( n ) ) } , $$\begin{aligned} &x^{(1)}(n+1)=\max_{1\le j\le l_{1}} \bigl\{ f_{1j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &x^{(2)}(n+1)=\max_{1\le j\le l_{2}} \bigl\{ f_{2j} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \\ &\vdots \\ &x^{(k)}(n+1)=\max_{1\le j\le l_{k}} \bigl\{ f_{kj} \bigl(n,x^{(1)}(n),\ldots ,x^{(k)}(n)\bigr) \bigr\} , \end{aligned}$$ n ∈ N 0 $n\in {\mathbb {N}}_{0}$ , where k ∈ N $k\in {\mathbb {N}}$ , l i ∈ N $l_{i}\in {\mathbb {N}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , x ( i ) ( 0 ) ∈ R $x^{(i)}(0)\in {\mathbb {R}}$ , i = 1 , k ‾ $i=\overline {1,k}$ , has a unique periodic solution attracting all the solutions to the system. Our main result considerably generalizes some recent results in the literature and simplifies their proofs. |
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