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Bifurcation Chaos"],"published-print":{"date-parts":[[2017,4]]},"abstract":"<jats:p> Chaos and chaos control of the Frenkel\u2013Kontorova (FK) model with dichotomous noise are studied theoretically and numerically. The threshold conditions for the onset of chaos in the FK model are firstly derived by applying the random Melnikov method with a mean-square criterion to the soliton equation, which is a fundamental topological mode of the FK model and accounts for its nonlinear phenomena. We found that dichotomous noise can induce stochastic chaos in the FK model, and the threshold of noise amplitude for the onset of chaos increases with the increase of its transition rate. Then the analytical criterion of chaos control is obtained by means of the time-delay feedback method. Since the time-delay feedback control raises the threshold of noise amplitude for the onset of chaos, chaos in the FK model is effectively suppressed. Through numerical simulations including the mean top Lyapunov exponent and the safe basin, we demonstrate the validity of the analytical predictions of chaos. Furthermore, time histories and phase portraits are utilized to verify the effectiveness of the proposed control. <\/jats:p>","DOI":"10.1142\/s0218127417500523","type":"journal-article","created":{"date-parts":[[2017,5,8]],"date-time":"2017-05-08T05:30:57Z","timestamp":1494221457000},"page":"1750052","source":"Crossref","is-referenced-by-count":17,"title":["Chaos and Chaos Control of the Frenkel\u2013Kontorova Model with Dichotomous Noise"],"prefix":"10.1142","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8078-1067","authenticated-orcid":false,"given":"Youming","family":"Lei","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, P. R. China"}]},{"given":"Fan","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, P. R. China"}]},{"given":"Xizhen","family":"Shao","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, P. R. 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