# 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

1993

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}, URL = {http://www.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://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2316.html %F Maistrenko:M93/26