{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:56:30Z","timestamp":1760784990888,"version":"3.41.2"},"reference-count":41,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,7,9]],"date-time":"2021-07-09T00:00:00Z","timestamp":1625788800000},"content-version":"vor","delay-in-days":189,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11572288"],"award-info":[{"award-number":["11572288"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>The complex bursting oscillation and bifurcation mechanisms in coupling systems of different scales have been a hot spot domestically and overseas. In this paper, we analyze the bursting oscillation of a generalized Duffing\u2013Van der Pol system with periodic excitation. Regarding this periodic excitation as a slow\u2010varying parameter, the system can possess two time scales and the equilibrium curves and bifurcation analysis of the fast subsystem with slow\u2010varying parameters are given. Through numerical simulations, we obtain four kinds of typical bursting oscillations, namely, symmetric fold\/fold bursting, symmetric fold\/supHopf bursting, symmetric subHopf\/fold cycle bursting, and symmetric subHopf\/subHopf bursting. It is found that these four kinds of bursting oscillations are symmetric. Combining the transformed phase portrait with bifurcation analysis, we can observe bursting oscillations obviously and further reveal bifurcation mechanisms of these four kinds of bursting oscillations.<\/jats:p>","DOI":"10.1155\/2021\/5556021","type":"journal-article","created":{"date-parts":[[2021,7,9]],"date-time":"2021-07-09T23:05:05Z","timestamp":1625871905000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Bursting Oscillation and Its Mechanism of a Generalized Duffing\u2013Van der Pol System with Periodic Excitation"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4562-9841","authenticated-orcid":false,"given":"Youhua","family":"Qian","sequence":"first","affiliation":[]},{"given":"Danjin","family":"Zhang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8528-7535","authenticated-orcid":false,"given":"Bingwen","family":"Lin","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,7,9]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-12316-5"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/100791233"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4766943"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1137\/070708810"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/080718528"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/11083678x"},{"key":"e_1_2_9_7_2","first-page":"228","article-title":"Series-mode pitchfork-hysteresis bursting oscillations and their dynamical mechanisms","volume":"51","author":"Zhang Y.","year":"2019","journal-title":"Chinese Journal of Theoretical and Applied Mechanics"},{"key":"e_1_2_9_8_2","first-page":"362","article-title":"Behaviors of modified Chua\u2019s oscillator two time scales under two excitations with frequency ratio at 1:2","volume":"50","author":"Xia Y.","year":"2018","journal-title":"Chinese Journal of Theoretical and Applied Mechanics"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2019.104924"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2020.297"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-011-0046-y"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.98.134101"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127419501347"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-019-05106-2"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2018.10.031"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10409-019-00923-5"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2020.103498"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/bfb0074739"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0960-0779(03)00027-4"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2011.01.037"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2009.08.020"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127418501468"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2018.02.031"},{"key":"e_1_2_9_24_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127419300283"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-019-05164-6"},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2019.07.032"},{"key":"e_1_2_9_27_2","first-page":"765","article-title":"Bursting phenomena as well as the bifurcation mechanism in periodically excited hartley model","volume":"42","author":"Chen Z. 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