Article ID Journal Published Year Pages File Type
1898809 Physica D: Nonlinear Phenomena 2009 14 Pages PDF
Abstract

We establish a lower bound on the measure of the set of stable parameters aa for the quadratic map Qa(x)=ax(1−x)Qa(x)=ax(1−x). For these parameters, we prove that QaQa either has a single stable periodic orbit or a period-doubling bifurcation. From this result, we also obtain a non-trivial upper bound on the set of stochastic parameters for QaQa.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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