On fourteen solvable systems of difference equations

Tollu, Durhasan Turgut; Yazlık, Yasin; Taşkara, Necati

doi:10.1016/j.amc.2014.02.001

Cited by 47 publications

(26 citation statements)

References 18 publications

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“…Some other results in the topic can be also found in other related works. [63][64][65][66][67][68][69][70][71][72] Special cases of the difference equation…”

Section: Introductionmentioning

confidence: 99%

Solvability and semi‐cycle analysis of a class of nonlinear systems of difference equations

Stević

Tollu

2019

Math Methods in App Sciences

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An analysis of semi‐cycles of positive solutions to eight systems of difference equations of the following form xn=a+pn−1qn−2pn−1+qn−2,yn=a+rn−1sn−2rn−1+sn−2,n∈double-struckN0, where a ∈ [0, + ∞), the sequences pn, qn, rn, sn are some of the sequences xn and yn, with positive initial values x−j,y−j, j = 1,2, is conducted in detail, and it is shown that these systems can be solved in closed‐form, which is the main result here. Two methods for showing the solvability are described.

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“…Some other results in the topic can be also found in other related works. [63][64][65][66][67][68][69][70][71][72] Special cases of the difference equation…”

Section: Introductionmentioning

confidence: 99%

Solvability and semi‐cycle analysis of a class of nonlinear systems of difference equations

Stević

Tollu

2019

Math Methods in App Sciences

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“…Also, for similar results in the area of difference equations and systems, see [4,10,[16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 96%

Dynamical behavior of a system of three-dimensional nonlinear difference equations

Okumuş

Soykan

2018

Adv Differ Equ

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“…In fact, countless papers have been published previously focusing on the aforementioned topic, see for example [5,6,7,16,20] and [21]. Interestingly, some of the solution forms of these equations are even expressible in terms of well-known integer sequences such as the Fibonacci numbers, Horadam numbers and Padovan numbers (see, e.g., [9,11,12,14,22,24,25,26,27,29,34]). …”

Section: Introductionmentioning

confidence: 99%

On the solutions of a higher‐order difference equation in terms of generalized Fibonacci sequences

Halim

Bayram

2015

Math Methods in App Sciences

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This paper deals with the solution, stability character and asymptotic behavior of the rational difference equationwhere N0 = N ∪ {0}, α, β, γ ∈ R + , and the initial conditions x−1 and x0 are non zero real numbers such that their solutions are associated to generalized Padovan numbers. Also, we investigate the two-dimensional case of the this equation given byand this generalizes the results presented in [34].

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On fourteen solvable systems of difference equations

Cited by 47 publications

References 18 publications

Solvability and semi‐cycle analysis of a class of nonlinear systems of difference equations

Solvability and semi‐cycle analysis of a class of nonlinear systems of difference equations

Dynamical behavior of a system of three-dimensional nonlinear difference equations

On the solutions of a higher‐order difference equation in terms of generalized Fibonacci sequences

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