A Closer Look at a Fibonacci-like Iterated Nonlinear Map: More Chaos and Order

P.R.J. Asveld

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    Abstract

    We continue our study of a Fibonacci-like analogue of the well-known iterated nonlinear map $x_{n+1}=\lambda x_n(1-x_n)$;cf. [1]. This second-order variant contains two parameters: viz. one which corresponds to $\lambda$, and a second one --denoted by $\alpha$-- that determines the relative influence of the two previous values. As in [1] we fix $\lambda$ to 3.9999 and we vary the parameter $\alpha$ from 0 to 1. We consider many subintervals of $\alpha$ --not mentioned in [1]-- that exhibit interesting types of behavior (regular patterns, periodic limit cycles, "intermediate stages", et cetera). The effect of the initial conditions on the ultimate behavior of this iterated mapping is also discussed. Keywords and phrases: dynamical system, nonlinearity, chaos, order, second-order difference equation, bifurcation. [1] P.R.J. Asveld, A Fibonacci-like Iterated Nonlinear Map or Order from Chaos in the Region of the Tiny Tornados, Memorandum Informatica 90-10 (1990), Dept. of Comp. Sci., Twente University of Technology.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente
    Number of pages66
    Publication statusPublished - 1991

    Publication series

    NameMemoranda informatica
    PublisherUniversity of Twente
    No.91-70
    ISSN (Print)0924-3755

    Keywords

    • HMI-SLT: Speech and Language Technology
    • Dynamical system
    • Nonlinearity
    • Chaos
    • Order
    • Second-order difference equation
    • Bifurcation
    • Initial conditions
    • Phase-plane portraits

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  • Cite this

    Asveld, P. R. J. (1991). A Closer Look at a Fibonacci-like Iterated Nonlinear Map: More Chaos and Order. (Memoranda informatica; No. 91-70). Enschede: University of Twente.