TY - BOOK

T1 - A Closer Look at a Fibonacci-like Iterated Nonlinear Map

T2 - More Chaos and Order

AU - Asveld, P.R.J.

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

KW - HMI-SLT: Speech and Language Technology

KW - Dynamical system

KW - Nonlinearity

KW - Chaos

KW - Order

KW - Second-order difference equation

KW - Bifurcation

KW - Initial conditions

KW - Phase-plane portraits

M3 - Report

T3 - Memoranda informatica

BT - A Closer Look at a Fibonacci-like Iterated Nonlinear Map

PB - University of Twente

CY - Enschede

ER -