Lo. Chua et al., A UNIVERSAL CIRCUIT FOR STUDYING AND GENERATING CHAOS .1. ROUTES TO CHAOS, IEEE transactions on circuits and systems. 1, Fundamental theory andapplications, 40(10), 1993, pp. 732-744
In this introductory tutorial paper, we demonstrate the generality of
Chua's oscillator in generating chaos and bifurcation phenomena by ele
ctronic laboratory experiments which illustrate the standard routes to
chaos, and by giving a result which shows that Chua's oscillator can
generate the same qualitative behavior as any member of a 21-parameter
family C of continuous, odd-symmetric, piecewise-linear vector field
in R3. This result is of fundamental importance because it unifies man
y previously published papers on chaotic circuits and systems (e.g. ex
amples from Brockett, Sparrow, Arneodo, Nishio, Ogorzalek, etc.) under
one umbrella, thereby obviating the need to analyze these circuits an
d systems as separate and unrelated systems. Indeed, every bifurcation
and chaotic phenomena exhibited by any member of the family C is also
exhibited by this universal circuit. In a companion paper [1], we sho
w how the generality of Chua's oscillator can be used to approximate o
ther chaotic systems in the literature which are not necessarily piece
wise-linear.