{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T07:15:04Z","timestamp":1768547704060,"version":"3.49.0"},"reference-count":29,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,13]],"date-time":"2023-12-13T00:00:00Z","timestamp":1702425600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"General Project of Guizhou Education University","award":["2022YB005"],"award-info":[{"award-number":["2022YB005"]}]},{"name":"General Project of Guizhou Education University","award":["QianJiaoJi[2022]029"],"award-info":[{"award-number":["QianJiaoJi[2022]029"]}]},{"name":"General Project of Guizhou Education University","award":["QianJiaoHeKY[2021]022"],"award-info":[{"award-number":["QianJiaoHeKY[2021]022"]}]},{"name":"General Project of Guizhou Education University","award":["QianJiaoJi-KY-Zi[2022]263"],"award-info":[{"award-number":["QianJiaoJi-KY-Zi[2022]263"]}]},{"name":"General Project of Guizhou Education University","award":["QianKeHeJiChu-ZK[2021]YiBan 309"],"award-info":[{"award-number":["QianKeHeJiChu-ZK[2021]YiBan 309"]}]},{"name":"Natural science research project of Guizhou Provincial Department of Education, China","award":["2022YB005"],"award-info":[{"award-number":["2022YB005"]}]},{"name":"Natural science research project of Guizhou Provincial Department of Education, China","award":["QianJiaoJi[2022]029"],"award-info":[{"award-number":["QianJiaoJi[2022]029"]}]},{"name":"Natural science research project of Guizhou Provincial Department of Education, China","award":["QianJiaoHeKY[2021]022"],"award-info":[{"award-number":["QianJiaoHeKY[2021]022"]}]},{"name":"Natural science research project of Guizhou Provincial Department of Education, China","award":["QianJiaoJi-KY-Zi[2022]263"],"award-info":[{"award-number":["QianJiaoJi-KY-Zi[2022]263"]}]},{"name":"Natural science research project of Guizhou Provincial Department of Education, China","award":["QianKeHeJiChu-ZK[2021]YiBan 309"],"award-info":[{"award-number":["QianKeHeJiChu-ZK[2021]YiBan 309"]}]},{"name":"Guizhou Education Department Youth Science and Technology Talent Growth Project","award":["2022YB005"],"award-info":[{"award-number":["2022YB005"]}]},{"name":"Guizhou Education Department Youth Science and Technology Talent Growth Project","award":["QianJiaoJi[2022]029"],"award-info":[{"award-number":["QianJiaoJi[2022]029"]}]},{"name":"Guizhou Education Department Youth Science and Technology Talent Growth Project","award":["QianJiaoHeKY[2021]022"],"award-info":[{"award-number":["QianJiaoHeKY[2021]022"]}]},{"name":"Guizhou Education Department Youth Science and Technology Talent Growth Project","award":["QianJiaoJi-KY-Zi[2022]263"],"award-info":[{"award-number":["QianJiaoJi-KY-Zi[2022]263"]}]},{"name":"Guizhou Education Department Youth Science and Technology Talent Growth Project","award":["QianKeHeJiChu-ZK[2021]YiBan 309"],"award-info":[{"award-number":["QianKeHeJiChu-ZK[2021]YiBan 309"]}]},{"DOI":"10.13039\/501100004001","name":"Science and Technology Foundation of Guizhou Province","doi-asserted-by":"publisher","award":["2022YB005"],"award-info":[{"award-number":["2022YB005"]}],"id":[{"id":"10.13039\/501100004001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004001","name":"Science and Technology Foundation of Guizhou Province","doi-asserted-by":"publisher","award":["QianJiaoJi[2022]029"],"award-info":[{"award-number":["QianJiaoJi[2022]029"]}],"id":[{"id":"10.13039\/501100004001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004001","name":"Science and Technology Foundation of Guizhou Province","doi-asserted-by":"publisher","award":["QianJiaoHeKY[2021]022"],"award-info":[{"award-number":["QianJiaoHeKY[2021]022"]}],"id":[{"id":"10.13039\/501100004001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004001","name":"Science and Technology Foundation of Guizhou Province","doi-asserted-by":"publisher","award":["QianJiaoJi-KY-Zi[2022]263"],"award-info":[{"award-number":["QianJiaoJi-KY-Zi[2022]263"]}],"id":[{"id":"10.13039\/501100004001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004001","name":"Science and Technology Foundation of Guizhou Province","doi-asserted-by":"publisher","award":["QianKeHeJiChu-ZK[2021]YiBan 309"],"award-info":[{"award-number":["QianKeHeJiChu-ZK[2021]YiBan 309"]}],"id":[{"id":"10.13039\/501100004001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this work, a novel conservative memristive chaotic system is constructed based on a smooth memristor. In addition to generating multiple types of quasi-periodic trajectories within a small range of a single parameter, the amplitude of the system can be controlled by changing the initial values. Moreover, the proposed system exhibits nonlinear dynamic characteristics, involving extreme multistability behavior of isomorphic and isomeric attractors. Finally, the proposed system is implemented using STMicroelectronics 32 and applied to image encryption. The excellent encryption performance of the conservative chaotic system is proven by an average correlation coefficient of 0.0083 and an information entropy of 7.9993, which provides a reference for further research on conservative memristive chaotic systems in the field of image encryption.<\/jats:p>","DOI":"10.3390\/e25121656","type":"journal-article","created":{"date-parts":[[2023,12,13]],"date-time":"2023-12-13T08:55:16Z","timestamp":1702457716000},"page":"1656","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Conservative Memristive Chaotic System with Extreme Multistability and Its Application in Image Encryption"],"prefix":"10.3390","volume":"25","author":[{"given":"Jian","family":"Li","sequence":"first","affiliation":[{"name":"College of Mathematics and Big Data, Guizhou Education University, Guiyang 550018, China"}]},{"given":"Bo","family":"Liang","sequence":"additional","affiliation":[{"name":"College of Big Data and Information Engineering, Guizhou University, Guiyang 550025, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0405-5944","authenticated-orcid":false,"given":"Xiefu","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Big Data, Guizhou Education University, Guiyang 550018, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5909-9883","authenticated-orcid":false,"given":"Zhixin","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Big Data, Guizhou Education University, Guiyang 550018, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1007\/s11071-021-07197-2","article-title":"A new 5D Hamiltonian conservative hyperchaotic system with four center type equilibrium points, wide range and coexisting hyperchaotic orbits","volume":"108","author":"Zhang","year":"2022","journal-title":"Nonlinear Dyn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2063","DOI":"10.1007\/s11071-018-4676-1","article-title":"Modelings and mechanism analysis underlying both the 4D Euler equations and Hamiltonian conservative chaotic systems","volume":"95","author":"Qi","year":"2019","journal-title":"Nonlinear Dyn."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3197","DOI":"10.1007\/s11071-020-05465-1","article-title":"Infinitely many coexisting conservative flows in a 4D conservative system inspired by LC circuit","volume":"99","author":"Wang","year":"2020","journal-title":"Nonlinear Dyn."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"154146","DOI":"10.1016\/j.aeue.2022.154146","article-title":"A memristive conservative chaotic circuit with two different offset boosting behaviors","volume":"147","author":"Du","year":"2022","journal-title":"AEU-Int. J. Electron. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"043111","DOI":"10.1063\/1.4946813","article-title":"Multistability in Chua\u2019s circuit with two stable node-foci","volume":"26","author":"Bao","year":"2016","journal-title":"Chaos Interdiscip. J. Nonlinear Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1140\/epjst\/e2015-02478-7","article-title":"Synchronization and multistability in the ring of modified R\u00f6ssler oscillators","volume":"224","author":"Jaros","year":"2015","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.chaos.2016.05.011","article-title":"Coexistence of multiple attractors and crisis route to chaos in a novel memristive diode bidge-based Jerk circuit","volume":"91","author":"Njitacke","year":"2016","journal-title":"Chaos Solitons Fractals"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1979","DOI":"10.1140\/epjst\/e2017-70037-1","article-title":"Megastability: Coexistence of a countable infinity of nested attractors in a periodically-forced oscillator with spatially-periodic damping","volume":"226","author":"Sprott","year":"2017","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1493","DOI":"10.1140\/epjst\/e2015-02475-x","article-title":"Multistability in symmetric chaotic systems","volume":"224","author":"Li","year":"2015","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"125207","DOI":"10.1088\/1402-4896\/ac9f87","article-title":"Coexistence of multiscroll chaotic attractors in two coupled inertial hopfield neurons: Numerical simulations and experiment","volume":"97","author":"Sriram","year":"2022","journal-title":"Phys. Scr."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1450034","DOI":"10.1142\/S0218127414500345","article-title":"Coexisting hidden attractors in a 4-D simplified Lorenz system","volume":"24","author":"Li","year":"2014","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"053127","DOI":"10.1063\/5.0008313","article-title":"Self-reproducing chaos and bursting oscillation analysis in a meminductor-based conservative system","volume":"30","author":"Yuan","year":"2020","journal-title":"Chaos Interdiscip. J. Nonlinear Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"7819","DOI":"10.1007\/s11071-022-08205-9","article-title":"A simple Hamiltonian conservative chaotic system with extreme multistability and offset-boosting","volume":"111","author":"Wang","year":"2023","journal-title":"Nonlinear Dyn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3812","DOI":"10.1007\/s00034-023-02322-5","article-title":"Design and Implementation of a Novel Circuit-Based Memristive Non-autonomous Hyperchaotic System with Conservative and Offset Boosting for Applications to Image Encryption","volume":"42","author":"Pratyusha","year":"2023","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"013110","DOI":"10.1063\/1.2430294","article-title":"A unified approach to attractor reconstruction","volume":"17","author":"Pecora","year":"2007","journal-title":"Chaos Interdiscip. J. Nonlinear Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"033111","DOI":"10.1063\/5.0066676","article-title":"A novel conservative system with hidden flows evolved from the simplest memristive circuit","volume":"32","author":"Yan","year":"2022","journal-title":"Chaos Interdiscip. J. Nonlinear Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1950021","DOI":"10.1142\/S0218127419500214","article-title":"Sprott, and Soroush Dehghan. Categories of conservative flows","volume":"29","author":"Jafari","year":"2019","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1681","DOI":"10.1007\/s11071-017-3758-9","article-title":"Hyperchaotic memristive system with hidden attractors and its adaptive control scheme","volume":"90","author":"Prousalis","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_19","first-page":"103367","article-title":"Quaternion with quantum walks for designing a novel color image cryptosystem","volume":"71","year":"2022","journal-title":"J. Inf. Secur. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4817","DOI":"10.1007\/s40747-023-00988-7","article-title":"Efficient S-box construction based on quantum-inspired quantum walks with PSO algorithm and its application to image cryptosystem","volume":"9","year":"2023","journal-title":"Complex Intell. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"169878","DOI":"10.1016\/j.ijleo.2022.169878","article-title":"A memristor-based VB2 chaotic system: Dynamical analysis, circuit implementation, and image encryption","volume":"269","author":"Hu","year":"2022","journal-title":"Optik"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"128624","DOI":"10.1016\/j.physa.2023.128624","article-title":"A 3D chaotic system with multi-transient behavior and its application in image encryption","volume":"616","author":"Liang","year":"2023","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s11071-016-3024-6","article-title":"An image encryption scheme combining chaos with cycle operation for DNA sequences","volume":"87","author":"Hu","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4957","DOI":"10.1109\/TCSI.2021.3121555","article-title":"Finite-\/fixed-time synchronization of memristor chaotic systems and image encryption application","volume":"68","author":"Wang","year":"2021","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2150251","DOI":"10.1142\/S0218127421502515","article-title":"Synchronization of a memristor chaotic system and image encryption","volume":"31","author":"Li","year":"2021","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1109\/TNSM.2020.2969863","article-title":"Secure data encryption based on quantum walks for 5G Internet of Things scenario","volume":"17","author":"Mazurczyk","year":"2020","journal-title":"IEEE Trans. Netw. Serv. Manag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"110504","DOI":"10.1088\/1674-1056\/abbbfe","article-title":"Memristor-based hyper-chaotic circuit for image encryption","volume":"29","author":"Chen","year":"2020","journal-title":"Chin. Phys. B"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhu, S., Deng, X., Zhang, W., and Zhu, C. (2021). A new one-dimensional compound chaotic system and its application in high-speed image encryption. Appl. Sci., 11.","DOI":"10.3390\/app112311206"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"20883","DOI":"10.1007\/s11042-021-10751-0","article-title":"A symmetric image encryption scheme based on hybrid analog-digital chaotic system and parameter selection mechanism","volume":"80","author":"Zheng","year":"2021","journal-title":"Multimed. Tools Appl."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/12\/1656\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:38:09Z","timestamp":1760132289000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/12\/1656"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,13]]},"references-count":29,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["e25121656"],"URL":"https:\/\/doi.org\/10.3390\/e25121656","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,13]]}}}