From Van der Pol to Chua: An introduction to nonlinear dynamics and chaos for second year undergraduates

This work shows how one can obtain Chua's circuit with a cubic nonlinearity from the classic Van der Pol oscillator. The approach helps in progressively advancing from the Hopf bifurcation phenomenon in the Van der Pol oscillator to the period-doubling bifurcations in Chua's circuit. We al...

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Bibliographic Details
Main Authors: Ambelang, S., Muthuswamy, B.
Format: Conference Proceeding
Language:English
Subjects:
Bifurcation
Chaos
Integrated circuit modeling
Mathematical model
Nonlinear dynamical systems
Oscillators
Resistors
Online Access:Request full text
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Description
Summary:This work shows how one can obtain Chua's circuit with a cubic nonlinearity from the classic Van der Pol oscillator. The approach helps in progressively advancing from the Hopf bifurcation phenomenon in the Van der Pol oscillator to the period-doubling bifurcations in Chua's circuit. We also place emphasis on mathematical simulation of the dynamic systemand physical circuit realization on a breadboard. This systematic methodology has proved invaluable in explaining the phenomenon of nonlinear dynamics and chaos to the curious undergraduate. The student is assumed to have a background in basic differential equations (equilibrium points, stability, linearization) and DC circuit theory. This paper is written with the student in mind. A student should be able to use this paper as a "two week lab manual" in an undergraduate course on nonlinear dynamcis and chaos.
ISSN:0271-4302
2158-1525
DOI:10.1109/ISCAS.2012.6271932