{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T08:34:14Z","timestamp":1648974854834},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,5]]},"abstract":"<jats:p> This paper presents an extended form of the high-dimensional Melnikov method for stochastically quasi-integrable Hamiltonian systems. A quasi-integrable Hamiltonian system with two degree-of-freedom (DOF) is employed to illustrate this extended approach, from which the stochastic Melnikov process is derived in detail when the harmonic and the bounded noise excitations are imposed on the system, and the mean-square criterion on the onset of chaos is then presented. It is shown that the threshold of the onset of chaos can be adjusted by changing the deterministic intensity of bounded noise, and one can find the range of the parameter related to the bandwidth of the bounded noise excitation where the chaotic motion can arise more readily by investigating the changes of the threshold region. Furthermore, some parameters are chosen to simulate the sample responses of the system according to the mean-square criterion from the extended stochastic Melnikov method, and the largest Lyapunov exponents are then calculated to identify these sample responses. <\/jats:p>","DOI":"10.1142\/s0218127412501179","type":"journal-article","created":{"date-parts":[[2012,3,29]],"date-time":"2012-03-29T01:21:56Z","timestamp":1332984116000},"page":"1250117","source":"Crossref","is-referenced-by-count":4,"title":["NOISY CHAOS IN A QUASI-INTEGRABLE HAMILTONIAN SYSTEM WITH TWO DOF UNDER HARMONIC AND BOUNDED NOISE EXCITATIONS"],"prefix":"10.1142","volume":"22","author":[{"given":"C. B.","family":"GAN","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Zhejiang University, Hangzhou 310027, P. R. China"}]},{"given":"Y. H.","family":"WANG","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Zhejiang University, Hangzhou 310027, P. R. China"}]},{"given":"S. X.","family":"YANG","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Zhejiang University, Hangzhou 310027, P. R. China"}]},{"given":"H.","family":"LEI","sequence":"additional","affiliation":[{"name":"Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2012,6,28]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12878-7"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408021129"},{"key":"rf3","volume-title":"Random Vibration in Mechanical Systems","author":"Crandal S. H.","year":"1963"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1115\/1.3167208"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/b97846"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405013149"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90114-G"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.11.070"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-005-9008-6"},{"key":"rf10","first-page":"066204-1","volume":"82","author":"Gan C. B.","journal-title":"Phys. Rev. E"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/9789814360586"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4286-4"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8928(83)90059-X"},{"key":"rf14","volume-title":"Probabilistic Structural Dynamics-Advanced Theory and Applications","author":"Lin Y. K.","year":"1995"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1115\/1.2788897"},{"key":"rf16","volume-title":"Random Vibration and Statistical Linearization","author":"Roberts J. B.","year":"1990"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90009-P"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9399(1996)122:3(263)"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-82863-8"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1016\/0022-460X(84)90515-7"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1042-9"},{"key":"rf23","first-page":"215","author":"Xie W. C.","journal-title":"Nonlin. Stochast. Dyn."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127412501179","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T16:14:05Z","timestamp":1565194445000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127412501179"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,5]]},"references-count":22,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2012,6,28]]},"published-print":{"date-parts":[[2012,5]]}},"alternative-id":["10.1142\/S0218127412501179"],"URL":"https:\/\/doi.org\/10.1142\/s0218127412501179","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,5]]}}}