# 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

1993

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}, URL = {http://www.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://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2290.html %F Kuznetsov:M93/15