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

EECS Department, University of California, Berkeley

Technical Report No. UCB/ERL M93/26

, 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.

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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},
    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