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Bounded solutions of a class of difference equations in Banach spaces producing controlled chaos

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  • Stević, Stevo

Abstract

Let X be a complex Banach space, αj, j=1,…,k, be real numbers, with ∑j=1kαj=1 and let (xn)n∈N be a sequence in X such thatlimn→∞xn+k-∑j=1kαjxn+k-j=0.It is given a sufficient and necessary condition such that the boundedness of (xn)n∈N always implies limn→∞∥xn+1−xn∥=0. We also present a sufficient condition which guarantees that every slowly varying solution of the difference equation xn+1=f(xn,…,xn−k) is convergent, if f is a real function.

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  • Stević, Stevo, 2008. "Bounded solutions of a class of difference equations in Banach spaces producing controlled chaos," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 238-245.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:2:p:238-245
    DOI: 10.1016/j.chaos.2007.07.037
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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. 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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