Shrimp Structure and Associated Dynamics in Parametrically Excited Oscillators

Y. Zou, Marco Thiel, M Carmen Romano, Q. Bi, Jurgen Kurths

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

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 Rényi entropy of second order K2, 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.

Original languageEnglish
Pages (from-to)3567-3579
Number of pages13
JournalInternational Journal of Bifurcation and Chaos
Volume16
Issue number12
DOIs
Publication statusPublished - 2006

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Convergence of numerical methods
Parameter Space
Large scale systems
Numerical analysis
Entropy
Bifurcation
Recurrence Plot
Period Doubling
Stable Solution
Intermittency
Chaotic Behavior
Numerical Analysis
Complex Systems
Degree of freedom

Cite this

Shrimp Structure and Associated Dynamics in Parametrically Excited Oscillators. / Zou, Y.; Thiel, Marco; Romano, M Carmen; Bi, Q.; Kurths, Jurgen.

In: International Journal of Bifurcation and Chaos, Vol. 16, No. 12, 2006, p. 3567-3579.

Research output: Contribution to journalArticle

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AU - Kurths, Jurgen

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