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

P.R.J. Asveld

Research output: Book/ReportReportOther research output

## 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 language English Enschede University of Twente 66 Published - 1991

### Publication series

Name Memoranda informatica University of Twente 91-70 0924-3755

## Keywords

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