Shrimp Structure and Associated Dynamics in Parametrically Excited Oscillators

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

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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
Issue number12
Publication statusPublished - 2006


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