Applied and Computational Mathematics

| Peer-Reviewed |

The Stability of High Order Max-Type Difference Equation

Received: 06 April 2016    Accepted:     Published: 07 April 2016
Views:       Downloads:

Share This Article

Abstract

In this paper, we investigate the stability of following max-type difference equation , where , with , , and , the initial values are positive. By constructing a system of equations and binary function, we show the equation has a unique positive equilibrium solution, and the positive equilibrium solution is globally asymptotically stable. The conclusion of this paper extends and supplements the existing results.

DOI 10.11648/j.acm.20160502.13
Published in Applied and Computational Mathematics (Volume 5, Issue 2, April 2016)
Page(s) 51-55
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Difference Equations, Positive Solution, Convergence, Globally Stable

References
[1] El-Metwally H, “Global behavior of an economic model,” Chaos Solitons & Fractals, 33(3), 2007, pp. 994-1005.
[2] El-Metwally H, El-Afifi M M, “On the behavior of some extension forms of some population Models,” Chaos Solitons & Fractals, 36(1), 2008, pp. 104-114.
[3] Zhou L, Honghua H U, Liang C, et al, “Research on difference equation model in traffic flow calculation,” Journal of Chang chun University of Science & Technology, 2014, pp. 117-123.
[4] Huang C M, Wang W P, “Applications of difference equation in population forecasting model,” Advanced Materials Research, 2014, pp. 1079-1080.
[5] Berenhaut K, Foley J, S. Stević S, “The global attractivity of the rational difference equation ,” Proceedings of the American Mathematical Society, 135, 2007, pp. 1133-1140.
[6] Berenhaut K S, Stević S, “The behavior of the positive solutions of the difference equation ,” J. Journal of Difference Equations and Applications, 12(9), 2006, pp. 909-918.
[7] Berg L, Stević S, “Periodicity of some classes of holomorphic difference equations,” Journal of Difference Equations and Applications, 12(8), 2006, pp. 827-835.
[8] Iričanin B, Stević S, “Some systems of nonlinear difference equations of higher order with periodic solutions,” Dynamics of Continuous Discrete and Impulsive Systems Series, 13A (3-4), 2006, pp. 499–507.
[9] Iričanin B, Stević S, “Eventually constant solutions of a rationa ldifference equation,” Applied Mathematics and Computation, 215, 2009, pp. 854-856.
[10] Elabbasy E M, El-Metwally H A, Elsayed E M, “Global behavior of the solutions of some difference equations,” Advances in Difference Equations, 28(2), 2011, pp. 683-689.
[11] Elsayed E M, Iričanin B, Stević S, “On the max-type equation ,” Ars Combinatoria, 95, 2010, pp. 187-192.
[12] Stević S, “Global stability of a max-type difference equation,” Applied Mathematics & Computation, 216(1), 2010, pp. 354–356.
[13] Sun T X, Xi H J, Han C H, “Dynamics of the max-type difference equation ,” Journal of Applied Mathematics and Computing, 2012 (1-2), 2012, pp. 173-180.
[14] Stević S, “On a symmetric system of max-type difference Equations,” Applied Mathematics and Computation, 219(15), 2013, pp. 8407-8412.
[15] Stević S, “On some periodic systems of max-type difference equations,” Applied Mathematics and Computation, 218, 2012, pp. 11483–11487.
[16] Amleh A M, Georgiou D A, Grove E A, Ladas G, “On the recursive sequence ,” Journal of Mathematital Analysis and applications, 233(2), 1999, pp. 790-798.
[17] Fan Y, Wang L, Li W, “Global behavior of a higher order nonlinear diference equation,” Journal of Mathematital Analysis and applications, 299(1), 2004, pp. 113-126.
[18] Sun T X, He Q L, Wua X, Xi H J, “Global behavior of the max-type difference equation ,” Applied Mathematics and Computation, 248, 2014, pp. 687-692.
[19] Liu W P, Stević S, “Global attractivity of a family of non-autonomous max-type difference equations,” Applied Mathematics and Computation, 218(11), 2012, pp. 6297-9303.
[20] Grove E A, Ladas G, Periodicities in Nonlinear Difference Equations, Vol. 4, New York: Chapman& Hall/CRC Press, 2005, pp. 2.
Author Information
  • School of Mathematics and Statistics, Guangxi Normal University, Guilin, China

  • School of Mathematics and Statistics, Guangxi Normal University, Guilin, China

  • School of Mathematics and Statistics, Guangxi Normal University, Guilin, China

Cite This Article
  • APA Style

    Han Cai-hong, Li Lue, Tan Xue. (2016). The Stability of High Order Max-Type Difference Equation. Applied and Computational Mathematics, 5(2), 51-55. https://doi.org/10.11648/j.acm.20160502.13

    Copy | Download

    ACS Style

    Han Cai-hong; Li Lue; Tan Xue. The Stability of High Order Max-Type Difference Equation. Appl. Comput. Math. 2016, 5(2), 51-55. doi: 10.11648/j.acm.20160502.13

    Copy | Download

    AMA Style

    Han Cai-hong, Li Lue, Tan Xue. The Stability of High Order Max-Type Difference Equation. Appl Comput Math. 2016;5(2):51-55. doi: 10.11648/j.acm.20160502.13

    Copy | Download

  • @article{10.11648/j.acm.20160502.13,
      author = {Han Cai-hong and Li Lue and Tan Xue},
      title = {The Stability of High Order Max-Type Difference Equation},
      journal = {Applied and Computational Mathematics},
      volume = {5},
      number = {2},
      pages = {51-55},
      doi = {10.11648/j.acm.20160502.13},
      url = {https://doi.org/10.11648/j.acm.20160502.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20160502.13},
      abstract = {In this paper, we investigate the stability of following max-type difference equation , where , with , ,  and , the initial values are positive. By constructing a system of equations and binary function, we show the equation has a unique positive equilibrium solution, and the positive equilibrium solution is globally asymptotically stable. The conclusion of this paper extends and supplements the existing results.},
     year = {2016}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - The Stability of High Order Max-Type Difference Equation
    AU  - Han Cai-hong
    AU  - Li Lue
    AU  - Tan Xue
    Y1  - 2016/04/07
    PY  - 2016
    N1  - https://doi.org/10.11648/j.acm.20160502.13
    DO  - 10.11648/j.acm.20160502.13
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
    SP  - 51
    EP  - 55
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20160502.13
    AB  - In this paper, we investigate the stability of following max-type difference equation , where , with , ,  and , the initial values are positive. By constructing a system of equations and binary function, we show the equation has a unique positive equilibrium solution, and the positive equilibrium solution is globally asymptotically stable. The conclusion of this paper extends and supplements the existing results.
    VL  - 5
    IS  - 2
    ER  - 

    Copy | Download

  • Sections