{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T00:47:43Z","timestamp":1779324463649,"version":"3.51.4"},"reference-count":44,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T00:00:00Z","timestamp":1745884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"High-Level Cultivation Project for Basic Research Business Expenses of Provincial Undergraduate Universities","award":["2023-KYYWF-0537"],"award-info":[{"award-number":["2023-KYYWF-0537"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In order to further explore the complex dynamical behavior involved in super-multistability, a new five-dimensional memristive chaotic system was obtained by using a magnetically controlled memristor to construct a four-dimensional equation on the basis of a three-dimensional chaotic system, adding a five-dimensional equation and selecting parameter y as the control term. Firstly, the multistability of the system was analyzed by using a Lyapunov exponential diagram, a bifurcation diagram and a phase portrait; the experimental results show that the system has parameter-related periodic chaotic alternating characteristics, symmetric attractors and transient chaotic characteristics, and it also has the characteristics of homogeneous multistability, heterogeneous multistability and super-multistability, which depend on the initial memristive values. Secondly, two offset constants g and h were added to the linear state variables, which were used as controllers of the attractors in the z and w directions, respectively, and the influences of the bidirectional offset increments on the system were analyzed. The complexity of the system was analyzed; the higher the complexity of the system, the larger the values of the complexity, and the darker the colors of the spectrogram. The five-dimensional memristive chaotic system was simulated using Multisim to verify the feasibility of the new system. Finally, an adaptive synchronization controller was designed using the method of adaptive synchronization; then, synchronization of the drive system and the response system was realized by changing the positive gain constant k, which achieved encryption and decryption of sinusoidal signals based on chaotic synchronization.<\/jats:p>","DOI":"10.3390\/e27050481","type":"journal-article","created":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T11:00:54Z","timestamp":1745924454000},"page":"481","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Analysis and Synchronous Study of a Five-Dimensional Multistable Memristive Chaotic System with Bidirectional Offset Increments"],"prefix":"10.3390","volume":"27","author":[{"given":"Lina","family":"Ding","sequence":"first","affiliation":[{"name":"School of Electronics and Information Engineering, Heilongjiang University of Science and Technology, Harbin 150022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-8705-463X","authenticated-orcid":false,"given":"Mengtian","family":"Xuan","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Heilongjiang University of Science and Technology, Harbin 150022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,29]]},"reference":[{"key":"ref_1","first-page":"191","article-title":"An amnesic chaotic system with super-multistability and its application in power image encryption","volume":"53","author":"Deng","year":"2024","journal-title":"Electromech. 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