{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T18:24:26Z","timestamp":1778610266544,"version":"3.51.4"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Lt","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,12]]},"abstract":"<jats:p> 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 R\u00e9nyi entropy of second order K<jats:sub>2<\/jats:sub>, 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. <\/jats:p>","DOI":"10.1142\/s0218127406016987","type":"journal-article","created":{"date-parts":[[2007,2,23]],"date-time":"2007-02-23T09:49:07Z","timestamp":1172224147000},"page":"3567-3579","source":"Crossref","is-referenced-by-count":31,"title":["SHRIMP STRUCTURE AND ASSOCIATED DYNAMICS IN PARAMETRICALLY EXCITED OSCILLATORS"],"prefix":"10.1142","volume":"16","author":[{"given":"Y.","family":"ZOU","sequence":"first","affiliation":[{"name":"Nonlinear Dynamics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"THIEL","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. 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