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Bifurcation Chaos"],"published-print":{"date-parts":[[2021,5]]},"abstract":"<jats:p> The pulse-shaped explosion (PSE), characterized by the pulse-shaped quantitative of system solutions varying dramatically, is a special route to bursting oscillations reported recently. This paper reports interesting dynamical behaviors related to the PSE of equilibria, and based on that, the complex bursting dynamics is investigated in a van der Pol\u2013Mathieu\u2013Duffing system with multiple-frequency slow-varying excitations. We find that bifurcations can be observed in a narrow parameter interval within PSE. We also show that two groups of bifurcations are symmetrically arranged on both sides of PSE, and each of which determines a different bursting part. Based on this, two compound bursting patterns, i.e. compound Hopf\/Hopf bursting oscillation and compound subHopf\/fold cycle bursting oscillation, and a novel type of relaxation oscillation (bursting oscillation of point\/point) independent of bifurcations, are revealed. Our results enrich the knowledge of dynamical behaviors related to PSE as well as the possible routes to complex bursting dynamics. <\/jats:p>","DOI":"10.1142\/s0218127421500826","type":"journal-article","created":{"date-parts":[[2021,5,28]],"date-time":"2021-05-28T08:30:07Z","timestamp":1622190607000},"page":"2150082","source":"Crossref","is-referenced-by-count":16,"title":["Complex Bursting Patterns in a van der Pol\u2013Mathieu\u2013Duffing Oscillator"],"prefix":"10.1142","volume":"31","author":[{"given":"Xindong","family":"Ma","sequence":"first","affiliation":[{"name":"Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China"}]},{"given":"Jin","family":"Song","sequence":"additional","affiliation":[{"name":"Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China"}]},{"given":"Mengke","family":"Wei","sequence":"additional","affiliation":[{"name":"Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China"}]},{"given":"Xiujing","family":"Han","sequence":"additional","affiliation":[{"name":"Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China"}]},{"given":"Qinsheng","family":"Bi","sequence":"additional","affiliation":[{"name":"Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. 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