On the Global Attractivity of a Max‐Type Difference Equation

Geli̇şken, Ali̇; Çınar, Cengiz

doi:10.1155/2009/812674

Cited by 13 publications

(8 citation statements)

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“…x � max A 1/(1+α) , B 1/(1+β) , when p � 1, k � 2. In 2009, Gelisken [17] proved that every positive solution of equation (2) converges to x � 1 or, eventually, periodic with period 2, when p � 1, k � 3, α � 1, and B � 1. In addition, in 1999, Szalkai [18] studied the periodicity of solutions of the following difference equation:…”

Section: Introductionmentioning

confidence: 99%

Periodic Solution for a Max-Type Fuzzy Difference Equation

Wang

2020

Journal of Mathematics

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The paper is concerned with the dynamics behavior of positive solutions for the following max-type fuzzy difference equation system: xn+1=maxA/xn, A/xn−1, xn−2, n=0,1,2,…, where xn is a sequence of positive fuzzy numbers, and the parameter A and the initial conditions x−2, x−1, x0 are also positive fuzzy numbers. Firstly, the fuzzy set theory is used to transform the fuzzy difference equation into the corresponding ordinary difference equations with parameters. Then, the expression for the periodic solution of the max-type ordinary difference equations is obtained by the iteration, the inequality technique, and the mathematical induction. Moreover, we can obtain the expression for the periodic solution of the max-type fuzzy difference equation. In addition, the boundedness and persistence of solutions for the fuzzy difference equation is proved. Finally, the results of this paper are simulated and verified by using MATLAB 2016 software package.

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Section: Introductionmentioning

confidence: 99%

Periodic Solution for a Max-Type Fuzzy Difference Equation

Wang

2020

Journal of Mathematics

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“…Recently, so called, max-type difference equations have attracted some attention (see, for example, [6,17,20] and the references therein) because the max operator have great importance in automatic control models (see, [15,19]) and have wide applications in biology (see, [8]), ecology (see, [12,18]), and physics (see, [4,10]). However, the maxima operator is not a smooth function in n-dimensional real vector space so that the techniques which use derivatives could be of almost no use, so the study of max-type systems of difference equations become more difficult.…”

Section: Introductionmentioning

confidence: 99%

On the periodicity of a max-type rational difference equation

Wang¹,

Jing²,

Hu³

et al. 2017

J. Nonlinear Sci. Appl.

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This paper shows that every well-defined solution of the following max-type difference equationwhere A ∈ R and the initial conditions x −2 , x −1 , x 0 are arbitrary non-zero real numbers is eventually periodic with period three by using new iteration method for the more general nonlinear difference equations and inequality skills as well as the mathematical induction. Our main results considerably improve results appearing in the literature.

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“…In recent years, the discrete case involving difference equations with maximum has been receiving increasing attention, for some results in this area; see, for example, [2–4]. …”

Section: Introductionmentioning

confidence: 99%

Eventually Periodic Solutions of a Max-Type Difference Equation

Sun

Liu

et al. 2014

The Scientific World Journal

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We study the following max-type difference equation x n = max⁡{A n/x n−r, x n−k}, n = 1,2,…, where {A n}n=1 +∞ is a periodic sequence with period p and k, r ∈ {1,2,…} with gcd(k, r) = 1 and k ≠ r, and the initial conditions x 1−d, x 2−d,…, x 0 are real numbers with d = max⁡{r, k}. We show that if p = 1 (or p ≥ 2 and k is odd), then every well-defined solution of this equation is eventually periodic with period k, which generalizes the results of (Elsayed and Stevic´ (2009), Iričanin and Elsayed (2010), Qin et al. (2012), and Xiao and Shi (2013)) to the general case. Besides, we construct an example with p ≥ 2 and k being even which has a well-defined solution that is not eventually periodic.

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On the Global Attractivity of a Max‐Type Difference Equation

Abstract: We investigate asymptotic behavior and periodic nature of positive solutions of the difference equation , where and . We prove that every positive solution of this difference equation approaches or is eventually periodic with period 2.

Cited by 13 publications

References 13 publications

Periodic Solution for a Max-Type Fuzzy Difference Equation

Periodic Solution for a Max-Type Fuzzy Difference Equation

On the periodicity of a max-type rational difference equation

Eventually Periodic Solutions of a Max-Type Difference Equation

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