A rigorous lower bound for the stability regions of the quadratic map

Warwick Tucker; Daniel Wilczak

doi:10.1016/j.physd.2009.06.020

A rigorous lower bound for the stability regions of the quadratic map

Warwick Tucker, Daniel Wilczak

Research output: Contribution to journal › Article › Research › peer-review

22 Citations (Scopus)

Abstract

We establish a lower bound on the measure of the set of stable parameters a for the quadratic map Q_a (x) = a x (1 - x). For these parameters, we prove that Q_a 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 Q_a.

Original language	English
Pages (from-to)	1923-1936
Number of pages	14
Journal	Physica D: Nonlinear Phenomena
Volume	238
Issue number	18
DOIs	https://doi.org/10.1016/j.physd.2009.06.020
Publication status	Published - Sept 2009
Externally published	Yes

Keywords

Interval analysis
Period-doubling bifurcation
Periodic orbit
Quadratic map

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10.1016/j.physd.2009.06.020

Cite this

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AU - Wilczak, Daniel

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AB - We establish a lower bound on the measure of the set of stable parameters a for the quadratic map Qa (x) = a x (1 - x). For these parameters, we prove that Qa 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 Qa.

KW - Interval analysis

KW - Period-doubling bifurcation

KW - Periodic orbit

KW - Quadratic map

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M3 - Article

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JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 18

ER -

A rigorous lower bound for the stability regions of the quadratic map

Abstract

Keywords

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