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Real-time finite difference bifurcation diagrams from analog electronic circuits

American Journal of Physics -- April 2004 -- Volume 72, Issue 4, pp. 499-502

Issue Date: April 2004
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KEYWORDS and PACS

Keywords
PACS
  • 01.50.-i
    Educational aids
  • 05.45.-a
    Nonlinear dynamics and nonlinear dynamical systems
  • YEAR: 2004

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PUBLICATION DATA

ISSN:
0002-9505 (print)  
Publisher:
AIP is a member of CrossRef AAPT
Edward H. Hellen
Department of Physics and Astronomy, University of North Carolina at Greensboro, Greensboro, North Carolina 27402
Bifurcation diagrams are a convenient way of displaying the variety of behaviors exhibited by nonlinear systems. One of the simplest nonlinear systems is a finite difference equation with a quadratic return map. This system exhibits a range of behaviors: stability, periodic oscillations, and chaos. We present simple inexpensive electronic circuits that perform analog computations of bifurcation diagrams for finite difference equations with quadratic return maps. These bifurcation diagrams, including one for the logistic equation, are easily displayed on an oscilloscope and agree well with analytical and computational predictions. ©2004 American Association of Physics Teachers.
History: Received 22 July 2003; accepted 25 November 2003
Permalink: http://dx.doi.org/10.1119/1.1643374

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