From Van der Pol to Chua: An Introduction to Nonlinear Dynamics and Chaos for Second Year Undergraduates

摘要

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 system and 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.