A Fibonacci-Like Iterated Nonlinear Map or Order from Chaos in the Region of the Tiny Tornados

P.R.J. Asveld

A Fibonacci-Like Iterated Nonlinear Map or Order from Chaos in the Region of the Tiny Tornados

P.R.J. Asveld

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Abstract

We study a Fibonacci-like variant of the well-known iterated nonlinear map
x_n+1 = λx_n(1-x_n). This second-order map contains two parameters of which one corresponds to λ, whereas the other one, denoted by a, determines the relative influence of the two previous values. Fixing λ to 3.9999 and varying the parameter a from 0 to 1 give rise to some interesting behavior. We focus our attention to the corresponding pictures rather than any underlying theoretical issue.

Original language	English
Place of Publication	Enschede
Publisher	University of Twente
Number of pages	45
Publication status	Published - 1990

Publication series

Name	Memoranda informatica
Publisher	University of Twente
No.	90-10
ISSN (Print)	0924-3755

Keywords

Dynamical system
Nonlinearity
Chaos
Order
Second-order difference equation
Bifurcation
HMI-SLT: Speech and Language Technology

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abstract = "We study a Fibonacci-like variant of the well-known iterated nonlinear map xn+1 = λxn(1-xn). This second-order map contains two parameters of which one corresponds to λ, whereas the other one, denoted by a, determines the relative influence of the two previous values. Fixing λ to 3.9999 and varying the parameter a from 0 to 1 give rise to some interesting behavior. We focus our attention to the corresponding pictures rather than any underlying theoretical issue.",

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N2 - We study a Fibonacci-like variant of the well-known iterated nonlinear map xn+1 = λxn(1-xn). This second-order map contains two parameters of which one corresponds to λ, whereas the other one, denoted by a, determines the relative influence of the two previous values. Fixing λ to 3.9999 and varying the parameter a from 0 to 1 give rise to some interesting behavior. We focus our attention to the corresponding pictures rather than any underlying theoretical issue.

AB - We study a Fibonacci-like variant of the well-known iterated nonlinear map xn+1 = λxn(1-xn). This second-order map contains two parameters of which one corresponds to λ, whereas the other one, denoted by a, determines the relative influence of the two previous values. Fixing λ to 3.9999 and varying the parameter a from 0 to 1 give rise to some interesting behavior. We focus our attention to the corresponding pictures rather than any underlying theoretical issue.

KW - Dynamical system

KW - Nonlinearity

KW - Chaos

KW - Order

KW - Second-order difference equation

KW - Bifurcation

KW - HMI-SLT: Speech and Language Technology

M3 - Report

T3 - Memoranda informatica

BT - A Fibonacci-Like Iterated Nonlinear Map or Order from Chaos in the Region of the Tiny Tornados

PB - University of Twente

CY - Enschede

ER -

A Fibonacci-Like Iterated Nonlinear Map or Order from Chaos in the Region of the Tiny Tornados

Abstract

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Keywords

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