Cycles of Chaotic Intervals in a 1-D Piecewise-Linear Map

Y.L. Maistrenko, V.L. Maistrenko and Leon O. Chua

EECS Department
University of California, Berkeley
Technical Report No. UCB/ERL M93/26
March 1993

http://www2.eecs.berkeley.edu/Pubs/TechRpts/1993/ERL-93-26.pdf

We study the bifurcations of attractors of a one-dimensional 2-segment piecewise linear map. We prove that the parameter regions of existence of stable point cycles y are separated by regions of existence of stable interval cycles I containing chaotic trajectories. Moreover, we show that the period-doubling phenomenon for stable interval cycles is characterized by two universal constants alpha and rho, whose values are calculated from explicit formulas.

BibTeX citation:

@techreport{Maistrenko:M93/26,
    Author = {Maistrenko, Y.L. and Maistrenko, V.L. and Chua, Leon O.},
    Title = {Cycles of Chaotic Intervals in a 1-D Piecewise-Linear Map},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1993},
    Month = {Mar},
    URL = {http://www2.eecs.berkeley.edu/Pubs/TechRpts/1993/2316.html},
    Number = {UCB/ERL M93/26},
    Abstract = {We study the bifurcations of attractors of a one-dimensional 2-segment piecewise linear map. We prove that the parameter regions of existence of stable point cycles y are separated by regions of existence of stable interval cycles I containing chaotic trajectories. Moreover, we show that the period-doubling phenomenon for stable interval cycles is characterized by two universal constants alpha and rho, whose values are calculated from explicit formulas.}
}

EndNote citation:

%0 Report
%A Maistrenko, Y.L.
%A Maistrenko, V.L.
%A Chua, Leon O.
%T Cycles of Chaotic Intervals in a 1-D Piecewise-Linear Map
%I EECS Department, University of California, Berkeley
%D 1993
%@ UCB/ERL M93/26
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/1993/2316.html
%F Maistrenko:M93/26