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Boundedness character of a fourth order nonlinear difference equation

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  • Stević, Stevo

Abstract

In this paper, among others, we give a complete picture of the boundedness character of the positive solutions of the following nonlinear difference equationxn+1=maxA,xnpxn-3p,n∈N0,where the parameters A and p are positive real numbers. This is a natural extension of a difference equation equivalent to an equation arising in automatic control theory. We present some new methods for investigating the boundedness character of nonlinear difference equations.

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  • Stević, Stevo, 2009. "Boundedness character of a fourth order nonlinear difference equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2364-2369.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2364-2369
    DOI: 10.1016/j.chaos.2007.10.030
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    References listed on IDEAS

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    1. Ishiyama, K. & Saiki, Y., 2005. "Unstable periodic orbits and chaotic economic growth," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 33-42.
    2. Taixiang Sun & Hongjian Xi & Hui Wu, 2006. "On boundedness of the solutions of the difference equation x n + 1 = x n − 1 / ( p + x n )," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-7, September.
    3. Ken-ichi Ishiyama & Yoshitaka Saiki, 2005. "Unstable periodic orbits embedded in a chaotic economic dynamics model," Applied Economics Letters, Taylor & Francis Journals, vol. 12(12), pages 749-753.
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    Cited by:

    1. Stević, Stevo, 2009. "On a class of higher-order difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 138-145.

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