{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:50:47Z","timestamp":1759942247314,"version":"3.41.2"},"reference-count":38,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,4,4]],"date-time":"2019-04-04T00:00:00Z","timestamp":1554336000000},"content-version":"vor","delay-in-days":93,"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":["11575036","11805021"],"award-info":[{"award-number":["11575036","11805021"]}],"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":[[2019,1]]},"abstract":"<jats:p>Though the complete chaos synchronization on single\u2010layer networks has been well understood, it is still a challenge on multiplex networks. In this work, we study the complete chaos synchronization on time\u2010dependent duplex networks in which interaction pattern among oscillators alternates periodically between two single\u2010layer networks. The alternations between two layers are characterized by the offset strength <jats:italic>A<\/jats:italic> and the switching frequency <jats:italic>\u03c9<\/jats:italic>. We find that there are two dynamical regimes depending on <jats:italic>\u03c9<\/jats:italic>. For high <jats:italic>\u03c9<\/jats:italic>, the critical <jats:italic>A<\/jats:italic> for the stable complete synchronization is independent of <jats:italic>\u03c9<\/jats:italic> and the fast\u2010switching approximation suggests that the time\u2010dependent duplex networks can be approximated by the time\u2010independent duplex networks with effective coupling strength. For low <jats:italic>\u03c9<\/jats:italic>, the critical <jats:italic>A<\/jats:italic> depends on <jats:italic>\u03c9<\/jats:italic> nonmonotonically. At extremely low <jats:italic>\u03c9<\/jats:italic>, the estimation of the critical <jats:italic>A<\/jats:italic> can be obtained by a single\u2010mode approximation taking one dominant transversal network mode to complete synchronization into considerations.<\/jats:p>","DOI":"10.1155\/2019\/6159365","type":"journal-article","created":{"date-parts":[[2019,4,5]],"date-time":"2019-04-05T00:16:01Z","timestamp":1554423361000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Chaos Synchronization in Time\u2010Dependent Duplex Networks"],"prefix":"10.1155","volume":"2019","author":[{"given":"Qian","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenchen","family":"Han","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lixing","family":"Lei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6120-4689","authenticated-orcid":false,"given":"Qionglin","family":"Dai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9290-1927","authenticated-orcid":false,"given":"Junzhong","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,4,4]]},"reference":[{"key":"e_1_2_8_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2008.09.002"},{"key":"e_1_2_8_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2005.859050"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/81.974874"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2003.10.052"},{"key":"e_1_2_8_5_2","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/81\/10006"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.63.036216"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4824312"},{"key":"e_1_2_8_8_2","doi-asserted-by":"publisher","DOI":"10.1209\/epl\/i2005-10533-0"},{"key":"e_1_2_8_9_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.76.1804"},{"key":"e_1_2_8_10_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.51.980"},{"key":"e_1_2_8_11_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.78.4193"},{"key":"e_1_2_8_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.2109"},{"key":"e_1_2_8_13_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.496"},{"key":"e_1_2_8_14_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.1601679"},{"key":"e_1_2_8_15_2","doi-asserted-by":"publisher","DOI":"10.1038\/srep00620"},{"key":"e_1_2_8_16_2","doi-asserted-by":"publisher","DOI":"10.1038\/srep01344"},{"key":"e_1_2_8_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2016.01.027"},{"key":"e_1_2_8_18_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNSE.2015.2425961"},{"key":"e_1_2_8_19_2","doi-asserted-by":"publisher","DOI":"10.1038\/nphys3865"},{"key":"e_1_2_8_20_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjb\/e2015-60270-7"},{"key":"e_1_2_8_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2014.07.001"},{"key":"e_1_2_8_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2008.09.045"},{"key":"e_1_2_8_23_2","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/14\/3\/033035"},{"key":"e_1_2_8_24_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2015.2468924"},{"key":"e_1_2_8_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.11.008"},{"key":"e_1_2_8_26_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.61.4877"},{"key":"e_1_2_8_27_2","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2006.887293"},{"key":"e_1_2_8_28_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0610245104"},{"key":"e_1_2_8_29_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.016102"},{"key":"e_1_2_8_30_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.100.044102"},{"key":"e_1_2_8_31_2","doi-asserted-by":"crossref","unstructured":"KingstonD. 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