{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,8]],"date-time":"2024-06-08T16:35:12Z","timestamp":1717864512761},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,1]]},"abstract":" We study the degenerate bifurcations of nonlinear normal modes (NNMs) of an unforced system consisting of a linear oscillator weakly coupled to an essentially nonlinear one. The potentials of both the oscillator and the coupling spring are adopted to be even-power polynomials with non-negative coefficients. Coupling parameter \u03b5 is defined and the bifurcations of the nonlinear normal modes structure with change of this coupling parameter are revealed. The degeneracy in the dynamics is manifested by a \"bifurcation from infinity\" where a saddle-node bifurcation point is generated at high energies, as perturbation of a state of infinite energy. Other (nondegenerate) saddle-node bifurcation points (at least one point) are generated in the vicinity of the point of exact 1 : 1 internal resonance between the linear and nonlinear oscillators. The above bifurcations form multiple-branch structure with few stable and unstable branches. This structure may disappear (for certain choices of the oscillator and coupling potentials) by the mechanism of successive cusp catastrophes with the growth of coupling parameter \u03b5. The above analytical findings are verified by means of direct numerical simulation (conservative Poincar\u00e9 sections). In the particular case of pure cubic nonlinearity of the oscillator and the coupling spring, an agreement between quantitative analytical predictions and numerical results is observed. <\/jats:p>","DOI":"10.1142\/s021812740601468x","type":"journal-article","created":{"date-parts":[[2006,3,3]],"date-time":"2006-03-03T11:45:38Z","timestamp":1141386338000},"page":"169-178","source":"Crossref","is-referenced-by-count":3,"title":["DEGENERATE BIFURCATION SCENARIOS IN THE DYNAMICS OF COUPLED OSCILLATORS WITH SYMMETRIC NONLINEARITIES"],"prefix":"10.1142","volume":"16","author":[{"given":"O. V.","family":"GENDELMAN","sequence":"first","affiliation":[{"name":"Faculty of Mechanical Engineering, Technion \u2014 Israel Institute of Technology, Haifa 32000, Israel"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02535-2"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1012967003477"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1115\/1.1345524"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025515112708"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-4799-0_24"},{"key":"rf6","volume-title":"Nonlinear Oscillations","author":"Nayfeh A. H.","year":"1984"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1002\/9783527617869"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1115\/1.1345525"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-460X(02)01207-5"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812740601468X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:08:03Z","timestamp":1565136483000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812740601468X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":9,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1142\/S021812740601468X"],"URL":"https:\/\/doi.org\/10.1142\/s021812740601468x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}