{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T07:22:26Z","timestamp":1763018546598,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T00:00:00Z","timestamp":1673827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61771176","2020J01395","2022J011203","2020-SSTD-005"],"award-info":[{"award-number":["61771176","2020J01395","2022J011203","2020-SSTD-005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundations of Fujian Province","award":["61771176","2020J01395","2022J011203","2020-SSTD-005"],"award-info":[{"award-number":["61771176","2020J01395","2022J011203","2020-SSTD-005"]}]},{"name":"innovation team of Wuyi University","award":["61771176","2020J01395","2022J011203","2020-SSTD-005"],"award-info":[{"award-number":["61771176","2020J01395","2022J011203","2020-SSTD-005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Based on a quantum logistic map and a Caputo-like delta difference operator, a fractional-order improved quantum logistic map, which has hidden attractors, was constructed. Its dynamical behaviors are investigated by employing phase portraits, bifurcation diagrams, Lyapunov spectra, dynamical mapping, and 0-1 testing. It is shown that the proposed fractional-order map is influenced by both the parameters and the fractional order. Then, the complexity of the map is explored through spectral entropy and approximate entropy. The results show that the fractional-order improved quantum logistic map has stronger robustness within chaos and higher complexity, so it is more suitable for engineering applications. In addition, the fractional-order chaotic map can be controlled for different periodic orbits by the improved nonlinear mapping on the wavelet function.<\/jats:p>","DOI":"10.3390\/axioms12010094","type":"journal-article","created":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T03:41:52Z","timestamp":1673926912000},"page":"94","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Fractional-Order Improved Quantum Logistic Map: Chaos, 0-1 Testing, Complexity, and Control"],"prefix":"10.3390","volume":"12","author":[{"given":"Birong","family":"Xu","sequence":"first","affiliation":[{"name":"College of Mechanic and Electronic Engineering, Wuyi University, Wuyishan 354300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ximei","family":"Ye","sequence":"additional","affiliation":[{"name":"College of Mechanic and Electronic Engineering, Wuyi University, Wuyishan 354300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6777-8234","authenticated-orcid":false,"given":"Guangyi","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongxian","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Computer Science, Wuyi University, Wuyishan 354300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changwu","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanic and Electronic Engineering, Wuyi University, Wuyishan 354300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1038\/261459a0","article-title":"Simple mathematical models with very complicated dynamics","volume":"261","author":"May","year":"1976","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2147","DOI":"10.1007\/s11071-019-05112-4","article-title":"Designing multi-dimensional logistic map with fixed-point finite precision","volume":"97","author":"Munir","year":"2019","journal-title":"Nonlinear Dyn."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1742","DOI":"10.1016\/j.physleta.2019.03.003","article-title":"On the dynamics of the q-deformed logistic map","volume":"383","year":"2019","journal-title":"Phys. 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