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.
| Author details: | Yong Zou, M. Thiel, Maria Carmen RomanoORCiD, Jürgen KurthsORCiDGND, Q. Bi |
|---|---|
| DOI: | https://doi.org/10.1142/S0218127406016987 |
| ISSN: | 0218-1274 |
| Title of parent work (English): | International journal of bifurcation and chaos : in applied sciences and engineering |
| Publisher: | World Scientific Publ. Co |
| Place of publishing: | Singapore |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2006/01/04 |
| Publication year: | 2006 |
| Release date: | 2020/04/16 |
| Tag: | bifurcation analysis; intermittency; period doubling; recurrence plot |
| Volume: | 16 |
| Issue: | 12 |
| Number of pages: | 13 |
| First page: | 3567 |
| Last Page: | 3579 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| Peer review: | Referiert |
| Institution name at the time of the publication: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik |
