{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T20:48:09Z","timestamp":1791924489343,"version":"4.3.4"},"reference-count":29,"publisher":"AIP Publishing","issue":"6","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12072291"],"award-info":[{"award-number":["12072291"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11732014"],"award-info":[{"award-number":["11732014"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12172306"],"award-info":[{"award-number":["12172306"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,6,1]]},"abstract":"<jats:p>Considering a piecewise linear oscillator with quasiperiodic excitation, we uncover the route of double grazing bifurcation of quasiperiodic torus to strange nonchaotic attractors (i.e., SNAs). The maximum displacement for double grazing bifurcation of the quasiperiodic torus can be obtained analytically. After double grazing of quasiperiodic orbits, the smooth quasiperiodic torus wrinkles increasingly with the continuous change of the parameter. Subsequently, the whole quasiperiodic torus loses the smoothness by becoming everywhere non-differentiable, which indicates the birth of SNAs. The Lyapunov exponent is adopted to verify the nonchaotic property of the SNA. The strange property of SNAs can be characterized by the phase sensitivity, the power spectrum, the singular continuous spectrum, and the fractal structure. Our detailed analysis shows that the SNAs induced by double grazing may exist in a short parameter interval between 1\u2009T quasiperiodic orbit and 2\u2009T quasiperiodic orbit or between 1\u2009T quasiperiodic orbit and 4\u2009T quasiperiodic orbit or between 1\u2009T quasiperiodic orbit and chaotic motion. Noteworthy, SNAs may also exist in a large parameter interval after double grazing, which does not lead to any quasiperiodic or chaotic orbits.<\/jats:p>","DOI":"10.1063\/5.0146285","type":"journal-article","created":{"date-parts":[[2023,6,25]],"date-time":"2023-06-25T03:21:52Z","timestamp":1687663312000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":7,"title":["Double grazing bifurcation route in a quasiperiodically driven piecewise linear oscillator"],"prefix":"10.1063","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-4122-8810","authenticated-orcid":false,"given":"Run","family":"Liu","sequence":"first","affiliation":[{"name":"Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Aerospace Engineering, Southwest Jiaotong University 1 , Chengdu 610031, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Celso","family":"Grebogi","sequence":"additional","affiliation":[{"name":"Institute for Complex Systems and Mathematical Biology King's College, University of Aberdeen 2 , Aberdeen AB24 3UE, United Kingdom"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8055-1851","authenticated-orcid":false,"given":"Yuan","family":"Yue","sequence":"additional","affiliation":[{"name":"Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Aerospace Engineering, Southwest Jiaotong University 1 , Chengdu 610031, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2023,6,23]]},"reference":[{"key":"2023062418411794200_c1","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/0022-460X(87)90361-0","article-title":"Global dynamics of a vibro-impacting linear oscillator","volume":"118","year":"1987","journal-title":"J. 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