{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,22]],"date-time":"2022-04-22T14:29:30Z","timestamp":1650637770211},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p> Bifurcations and chaos of Duffing\u2013van der Pol equation with nonsymmetric nonlinear restoring and two external forcing terms are investigated. The threshold values of the existence of chaotic motion are obtained under periodic perturbation. By the second-order averaging method, we prove the criteria of the existence of chaos in an averaged system under quasi-periodic perturbation for \u03c9<jats:sub>2<\/jats:sub> = n\u03c9<jats:sub>1<\/jats:sub> + \u03b5\u03c3, n = 1, 2, 3, 5, and cannot prove the criterion of existence of chaos in an averaged system under quasi-periodic perturbation for \u03c9<jats:sub>2<\/jats:sub> = n\u03c9<jats:sub>1<\/jats:sub> + \u03b5\u03c3, n = 4, 6, 7, \u2026, where \u03c3 is not rational to \u03c9<jats:sub>1<\/jats:sub>, but can show the occurrence of chaos in the original system by numerical simulation. Numerical simulation including homoclinic or heteroclinic bifurcation surfaces, bifurcation diagrams, maximal Lyapunov exponents, phase portraits and Poincar\u00e9 maps, not only show the consistence with the theoretical analysis but also exhibit more new complex dynamical behaviors. We show that cascades of interlocking period-doubling and reverse period-doubling bifurcations lead to interleaving occurrence of chaotic behaviors and quasi-periodic orbits, symmetry-breaking of periodic orbits in chaotic regions, onset of chaos occurring more than once, chaos suddenly disappearing to periodic orbits, strange nonchaotic attractor, nonattracting chaotic set and nice chaotic attractors. <\/jats:p>","DOI":"10.1142\/s0218127414300110","type":"journal-article","created":{"date-parts":[[2014,3,25]],"date-time":"2014-03-25T05:36:36Z","timestamp":1395725796000},"page":"1430011","source":"Crossref","is-referenced-by-count":3,"title":["Bifurcations and Chaos of Duffing\u2013van der Pol Equation with Nonsymmetric Nonlinear Restoring and Two External Forcing Terms"],"prefix":"10.1142","volume":"24","author":[{"given":"Zhiyan","family":"Yang","sequence":"first","affiliation":[{"name":"School of Information, Beijing Wuzi University, Beijing 101149, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Information, Beijing Wuzi University, Beijing 101149, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhujun","family":"Jing","sequence":"additional","affiliation":[{"name":"Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. 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