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We show that for rational relations of the frequencies the system develops several rotational excitations with right\/left symmetry, corresponding to limit cycles in the four-dimensional phase space. The corresponding noisy distributions have the form of hoops or tires in the four-dimensional space. For irrational frequency relations, as well as for increasing strength of driving or noise the periodic excitations are replaced by chaotic oscillations. <\/jats:p>","DOI":"10.1142\/s0218127405014271","type":"journal-article","created":{"date-parts":[[2006,2,6]],"date-time":"2006-02-06T04:49:18Z","timestamp":1139201358000},"page":"3623-3633","source":"Crossref","is-referenced-by-count":13,"title":["ON THE ATTRACTORS OF TWO-DIMENSIONAL RAYLEIGH OSCILLATORS INCLUDING NOISE"],"prefix":"10.1142","volume":"15","author":[{"given":"UDO","family":"ERDMANN","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Physik, Humboldt-Universit\u00e4t zu Berlin, Newtonstr. 15, 12489 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"WERNER","family":"EBELING","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Physik, Humboldt-Universit\u00e4t zu Berlin, Newtonstr. 15, 12489 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.77.2129"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/9789812833693"},{"key":"rf3","series-title":"Springer Series in Synergetics","volume-title":"Nonlinear Dynamics of Chaotic and Stochastic Systems","author":"Anishchenko V. 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