Property of period-doubling bifurcations

Liqiu Wang and Mingtian Xu

Chaos, Solitons & Fractals, 2005, vol. 24, issue 2, 527-532

Abstract: The period-doubling bifurcation leads a T-periodic solution to a 2T-periodic solution. We develop the relation between these two periodic solutions analytically for a general parameter-dependent dynamic system. Such the relation is further confirmed by one example and shows that the 2T-periodic solution contains all the information of the T-periodic solution near the bifurcation point. Therefore we can infer the T-periodic solution from the 2T-periodic solution. Conversely, we may obtain the part of the 2T-periodic solution from the T-periodic solution. The work sheds light on the period-doubling bifurcation and chaos in general, the self-similarity of chaotic solutions in particular, forms a benchmark of numerical accuracy checking and provides new numerical schemes of period-doubling bifurcation detection.

Date: 2005
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:24:y:2005:i:2:p:527-532

DOI: 10.1016/j.chaos.2004.09.045

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