Self-Similarity and Universality in Chua's Circuit via the Approximate Chua's 1-D Map

A.P. Kuznetsov, S.P. Kuznetsov, I.R. Sataev and Leon O. Chua

EECS Department
University of California, Berkeley
Technical Report No. UCB/ERL M93/15
February 1993

http://www2.eecs.berkeley.edu/Pubs/TechRpts/1993/ERL-93-15.pdf

In this paper we investigate the features of the transition to chaos in a one-dimensional Chua's map which describes approximately the Chua's circuit. These features arise from the nonunimodality of this map. We show that there exists a variety of types of critical points, which are characterized by a universal self-similar topography in a neighborhood of each critical point in the parameter plane. Such universalities are associated with various cycles of the Feigenbaum's renormalization group equation.

BibTeX citation:

@techreport{Kuznetsov:M93/15,
    Author = {Kuznetsov, A.P. and Kuznetsov, S.P. and Sataev, I.R. and Chua, Leon O.},
    Title = {Self-Similarity and Universality in Chua's Circuit via the Approximate Chua's 1-D Map},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1993},
    Month = {Feb},
    URL = {http://www2.eecs.berkeley.edu/Pubs/TechRpts/1993/2290.html},
    Number = {UCB/ERL M93/15},
    Abstract = {In this paper we investigate the features of the transition to chaos in a one-dimensional Chua's map which describes approximately the Chua's circuit. These features arise from the nonunimodality of this map. We show that there exists a variety of types of critical points, which are characterized by a universal self-similar topography in a neighborhood of each critical point in the parameter plane. Such universalities are associated with various cycles of the Feigenbaum's renormalization group equation.}
}

EndNote citation:

%0 Report
%A Kuznetsov, A.P.
%A Kuznetsov, S.P.
%A Sataev, I.R.
%A Chua, Leon O.
%T Self-Similarity and Universality in Chua's Circuit via the Approximate Chua's 1-D Map
%I EECS Department, University of California, Berkeley
%D 1993
%@ UCB/ERL M93/15
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/1993/2290.html
%F Kuznetsov:M93/15