Eventually Periodic Solutions of a Max-Type Difference Equation

Sun, Taixiang; Liu, Jing; Liu, Xinhe; Tao, Chunyan

doi:10.1155/2014/219437

Cited by 12 publications

(7 citation statements)

References 7 publications

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“…Recently, Xiao and Shi [24] studied equation 5, when k � 1, and the result that every well-defined solution is eventually periodic with period 2 is obtained. Because of the necessity for some techniques, in 2014, Sun et al [25] considered the following max-type equation that extends the form of equation (5):…”

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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“…Because of this, scholars have studied many theories and applications of the max-type difference equation in recent years. Since periodical research of differential equation theory has been very mature and perfect, some scholars try to investigate the periodicity of difference equation with the theory of differential equation (see, e.g., [11][12][13][14][15][16][17] and the reference therein).…”

Section: Introductionmentioning

confidence: 99%

On the Periodicity of a Max-type Fuzzy Difference Equations

Wang¹,

Wei²,

Yang³

et al. 2019

AJEA

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Our aim in this paper is to discuss the periodicity and boundedness of a max-type fuzzy difference equation. When studying the periodicity of the solution to the max-fuzzy difference equation, the equation is first converted into a difference system composed of two related difference equations through the cut set theory of the fuzzy number, then the periodicity of each solution sequence in the system is obtained by means of inequality technique, mathematical induction and other theoretical methods, thus the periodicity of the solution is proved. As researching the boundedness of the solution for the fuzzy difference equation, the difference system is also obtained through the cut set theory of the fuzzy number, then analyze the boundedness to each solution sequence according to the periodicity with the solution sequence, through examining the value of the finite subsequence in each solution sequence, the boundedness with these subsequences can be obtained, and then the boundedness for each solution sequence made up of complete subsequences can be known, thus the boundedness of the solution is proved. Finally, the results obtained in this paper are simulated by using the software package MATLAB 2016, the numerical results not only show the dynamic behavior of the solutions to the fuzzy difference systems, but also verify the effectiveness of the theoretical results.

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“…They showed that every positive solution of (1.7) is eventually periodic with period sT for some T ∈ N if f ji j satisfy some conditions. For some results of some properties of many max-type difference equations and systems, such as eventual periodicity, the boundedness character, and attractivity, see, e.g., [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and the related references therein.…”

Section: Introductionmentioning

confidence: 99%