{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:17:18Z","timestamp":1760188638154,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T00:00:00Z","timestamp":1557446400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Scientific Research Plan of Universities in Shandong Province","award":["Grant No. J18KA352"],"award-info":[{"award-number":["Grant No. J18KA352"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>By designing a state observer, a new type of synchronization named complex modified projective synchronization is investigated in a class of nonlinear fractional-order complex chaotic systems. Combining stability results of the fractional-order systems and the pole placement method, this paper proves the stability of fractional-order error systems and realizes complex modified projective synchronization. This method is so effective that it can be applied in engineering. Additionally, the proposed synchronization strategy is suitable for all fractional-order chaotic systems, including fractional-order hyper-chaotic systems. Finally, two numerical examples are studied to show the correctness of this new synchronization strategy.<\/jats:p>","DOI":"10.3390\/e21050481","type":"journal-article","created":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T11:00:57Z","timestamp":1557745257000},"page":"481","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers"],"prefix":"10.3390","volume":"21","author":[{"given":"Zhonghui","family":"Li","sequence":"first","affiliation":[{"name":"Business School, Shandong Normal University, Jinan 250014, China"}]},{"given":"Tongshui","family":"Xia","sequence":"additional","affiliation":[{"name":"Business School, Shandong Normal University, Jinan 250014, China"}]},{"given":"Cuimei","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1016\/j.chaos.2004.09.090","article-title":"Chaos in the fractional order periodically forced complex Duffing\u2019s oscillators","volume":"24","author":"Gao","year":"2005","journal-title":"Chaos Solitons Fractals"},{"key":"ref_2","first-page":"1","article-title":"Dynamic properties of the fractional-order Logistic equation of complex variables","volume":"2012","author":"Ahmed","year":"2012","journal-title":"Abstr. 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