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Shrimp structure and associated dynamics in parametrically excited oscillators

  • We investigate the bifurcation structures in a two-dimensional parameter space (PS) of a parametrically excited system with two degrees of freedom both analytically and numerically. By means of the Renyi entropy of second order K-2, which is estimated from recurrence plots, we uncover that regions of chaotic behavior are intermingled with many complex periodic windows, such as shrimp structures in the PS. A detailed numerical analysis shows that, the stable solutions lose stability either via period doubling, or via intermittency when the parameters leave these shrimps in different directions, indicating different bifurcation properties of the boundaries. The shrimps of different sizes offer promising ways to control the dynamics of such a complex system.

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Author:Yong Zou, M. Thiel, Maria Carmen RomanoORCiD, Jürgen KurthsORCiDGND, Q. Bi
Parent Title (English):International journal of bifurcation and chaos : in applied sciences and engineering
Publisher:World Scientific Publ. Co
Place of publication:Singapore
Document Type:Article
Date of first Publication:2006/01/04
Year of Completion:2006
Release Date:2020/04/16
Tag:bifurcation analysis; intermittency; period doubling; recurrence plot
Page Number:13
First Page:3567
Last Page:3579
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer Review:Referiert
Institution name at the time of publication:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik