{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T13:47:25Z","timestamp":1779371245214,"version":"3.53.1"},"reference-count":46,"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":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12462004"],"award-info":[{"award-number":["12462004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12262024"],"award-info":[{"award-number":["12262024"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2023JBBJ004"],"award-info":[{"award-number":["2023JBBJ004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022MS01003"],"award-info":[{"award-number":["2022MS01003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Inner Mongolia Normal University","award":["12462004"],"award-info":[{"award-number":["12462004"]}]},{"name":"Fundamental Research Funds for the Inner Mongolia Normal University","award":["12262024"],"award-info":[{"award-number":["12262024"]}]},{"name":"Fundamental Research Funds for the Inner Mongolia Normal University","award":["2023JBBJ004"],"award-info":[{"award-number":["2023JBBJ004"]}]},{"name":"Fundamental Research Funds for the Inner Mongolia Normal University","award":["2022MS01003"],"award-info":[{"award-number":["2022MS01003"]}]},{"name":"Natural Science Foundation of Inner Mongolia Autonomous Region","award":["12462004"],"award-info":[{"award-number":["12462004"]}]},{"name":"Natural Science Foundation of Inner Mongolia Autonomous Region","award":["12262024"],"award-info":[{"award-number":["12262024"]}]},{"name":"Natural Science Foundation of Inner Mongolia Autonomous Region","award":["2023JBBJ004"],"award-info":[{"award-number":["2023JBBJ004"]}]},{"name":"Natural Science Foundation of Inner Mongolia Autonomous Region","award":["2022MS01003"],"award-info":[{"award-number":["2022MS01003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Introducing a memristor into chaotic systems facilitates the construction of high-dimensional hyperchaotic systems. The hyperchaotic signals generated by these systems have important applications in the field of information security. A five-dimensional hyperchaotic system is constructed by introducing a memristor. Its hyperchaotic nature is discussed using phase diagrams and Lyapunov exponential diagrams. The effects of the parameters on the dynamical behavior are examined by bifurcation diagrams and Lyapunov exponential diagrams. To validate the theoretical model, an electronic circuit was designed for circuit simulation. The electronic simulation of the circuit was carried out using the Multisim simulation platform. Finally, the fixed-time projection synchronization of the system was taken into consideration. Three sets of synchronization schemes were considered and simulated. The synchronization scheme has the features of fast synchronization speed and robustness. It is potentially valuable for applications in the fields of chaotic communication and chaotic encryption.<\/jats:p>","DOI":"10.3390\/sym17050685","type":"journal-article","created":{"date-parts":[[2025,5,4]],"date-time":"2025-05-04T20:42:37Z","timestamp":1746391357000},"page":"685","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Dynamics, Circuit Simulation and Fixed-Time Projection Synchronization in a Memristor-Based Hyperchaotic System"],"prefix":"10.3390","volume":"17","author":[{"given":"Yan","family":"Zhou","sequence":"first","affiliation":[{"name":"College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China"},{"name":"Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application, Hohhot 010022, China"},{"name":"Center for Applied Mathematical Science, Hohhot 010022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruimei","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhuang","family":"Cui","sequence":"additional","affiliation":[{"name":"College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/s11045-021-00814-8","article-title":"Image encryption based on 5D hyperchaotic system using hybrid random matrix transform","volume":"33","author":"Sheela","year":"2022","journal-title":"Multidimens. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2891","DOI":"10.1007\/s12555-022-0909-7","article-title":"A Robust Underactuated Synchronizer for a Five-dimensional Hyperchaotic System: Applications for Secure Communication","volume":"21","author":"Gularte","year":"2023","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1109\/TCT.1971.1083337","article-title":"Memristor-the missing circuit element","volume":"18","author":"Chua","year":"1971","journal-title":"IEEE Trans. Circuit Theory"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1038\/nature06932","article-title":"The missing memristor found","volume":"453","author":"Strukov","year":"2008","journal-title":"Nature"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Butusov, D.N., Karimov, A.I., Pesterev, D.O., Tutueva, A.V., and Okoli, G. (February, January 29). Bifurcation and recurrent analysis of memristive circuits. Proceedings of the 2018 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus), Moscow, Russia.","DOI":"10.1109\/EIConRus.2018.8317059"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ostrovskii, V.Y., Tutueva, A.V., Rybin, V.G., Karimov, A.I., and Butusov, D.N. (2020, January 3\u20136). Continuation analysis of memristor-based modified Chua\u2019s circuit. Proceedings of the 2020 International Conference Nonlinearity, Information and Robotics (NIR), Innopolis, Russia.","DOI":"10.1109\/NIR50484.2020.9290157"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ostrovskii, V., Fedoseev, P., Bobrova, Y., and Butusov, D. (2022). Structural and Parametric Identification of Knowm Memristors. Nanomaterials, 12.","DOI":"10.3390\/nano12010063"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wu, X.M., He, S.B., Tan, W.J., and Wang, H.H. (2022). From memristor-modeled jerk system to the nonlinear systems with memristor. Symmetry, 14.","DOI":"10.3390\/sym14040659"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1750027","DOI":"10.1142\/S0218127417500274","article-title":"Generating four-wing hyperchaotic attractor and two-wing, three-wing, and four-wing chaotic attractors in 4D memristive system","volume":"27","author":"Zhou","year":"2017","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1007\/s11431-015-5981-2","article-title":"A novel memristive neural network with hidden attractors and its circuitry implementation","volume":"59","author":"Pham","year":"2016","journal-title":"Sci. China Technol. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"105639","DOI":"10.1016\/j.mejo.2022.105639","article-title":"An FPGA-based memristor emulator for artificial neural network","volume":"131","author":"Zhang","year":"2023","journal-title":"Microelectron. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2629","DOI":"10.1142\/S0218127411029999","article-title":"A simple memristor chaotic circuit with complex dynamics","volume":"21","author":"Bao","year":"2011","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1850038","DOI":"10.1142\/S021812661850038X","article-title":"The design and realization of a hyper-chaotic circuit based on a flux-controlled memristor with linear memductance","volume":"27","author":"Wang","year":"2018","journal-title":"J. Circuits Syst. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.vlsi.2022.09.004","article-title":"A new 4D Memristor chaotic system: Analysis and implementation","volume":"88","author":"Messadi","year":"2023","journal-title":"Integration"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2653","DOI":"10.1007\/s11071-016-2852-8","article-title":"Generating hyperchaotic multi-wing attractor in a 4D memristive circuit","volume":"85","author":"Zhou","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1750091","DOI":"10.1142\/S0218127417500912","article-title":"A memristive hyperchaotic multiscroll jerk system with controllable scroll numbers","volume":"27","author":"Wang","year":"2017","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"107085","DOI":"10.1016\/j.rinp.2023.107085","article-title":"Dynamical analysis and synchronization control of flux-controlled memristive chaotic circuits and its FPGA-Based implementation","volume":"54","author":"Luo","year":"2023","journal-title":"Results Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"113440","DOI":"10.1016\/j.chaos.2023.113440","article-title":"Bifurcation, chaos and fixed-time synchronization of memristor cellular neural networks","volume":"171","author":"Chen","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"073107","DOI":"10.1063\/1.4958296","article-title":"Extreme multistability in a memristor-based multi-scroll hyper-chaotic system","volume":"26","author":"Yuan","year":"2016","journal-title":"Chaos"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3029","DOI":"10.1140\/epjs\/s11734-022-00639-x","article-title":"Dynamic analysis and circuit realization of a novel variable-wing 5D memristive hyperchaotic system with line equilibrium","volume":"231","author":"Wan","year":"2022","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"015243","DOI":"10.1088\/1402-4896\/ad173d","article-title":"A novel 5D memristor conservative chaotic system with multiple forms of hidden flows","volume":"99","author":"Xu","year":"2023","journal-title":"Phys. Scr."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"070505","DOI":"10.1088\/1674-1056\/ac4a71","article-title":"Design and FPGA implementation of a memristor-based multi-scroll hyperchaotic system","volume":"31","author":"Jia","year":"2022","journal-title":"Chin. Phys. B"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Yu, F., Zhang, W.X., Xiao, X.L., Yao, W., Cai, S., Zhang, J., Wang, C.H., and Li, Y. (2023). Dynamic analysis and FPGA implementation of a new, simple 5D memristive hyperchaotic Sprott-C system. Mathematics, 11.","DOI":"10.3390\/math11030701"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"124641","DOI":"10.1109\/ACCESS.2019.2938183","article-title":"An optimized memristor-based hyperchaotic system with controlled hidden attractors","volume":"7","author":"Min","year":"2019","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2250090","DOI":"10.1142\/S0217984922500907","article-title":"Symmetric extreme multistability and memristor initial-offset boosting in a new 5D four-wing hyperchaotic system based on dual memristors","volume":"36","author":"Li","year":"2022","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"107201","DOI":"10.1016\/j.rinp.2023.107201","article-title":"A 3D memristor-based chaotic system with transition behaviors of coexisting attractors between equilibrium points","volume":"56","author":"Wang","year":"2024","journal-title":"Results Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/j.cjph.2021.03.009","article-title":"Synchronization, circuit and secure communication implementation of a memristor-based hyperchaotic system using single input controller","volume":"71","author":"Luo","year":"2021","journal-title":"Chin. J. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"025210","DOI":"10.1088\/1402-4896\/ad1567","article-title":"Hidden extreme multistability in a smooth flux-controlled memristor based four-dimensional chaotic system and its application in image encryption","volume":"99","author":"Tamba","year":"2024","journal-title":"Phys. Scr."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.vlsi.2023.01.006","article-title":"Dynamics analysis, FPGA realization and image encryption application of a 5D memristive exponential hyperchaotic system","volume":"90","author":"Yu","year":"2023","journal-title":"Integration"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3042","DOI":"10.1103\/PhysRevLett.82.3042","article-title":"Projective synchronization in three-dimensional chaotic systems","volume":"82","author":"Mainieri","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1007\/s12043-023-02544-x","article-title":"Dynamical analysis of a 5D novel system based on Lorenz system and its hybrid function projective synchronisation using adaptive control","volume":"97","author":"Khattar","year":"2023","journal-title":"Pramana J. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3617","DOI":"10.1007\/s12648-023-02702-2","article-title":"Finite-time projective synchronization of complex networks via adaptive control","volume":"97","author":"Lai","year":"2023","journal-title":"Indian J. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2106","DOI":"10.1109\/TAC.2011.2179869","article-title":"Nonlinear feedback design for fixed-time stabilization of linear control systems","volume":"57","author":"Polyakov","year":"2011","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"127388","DOI":"10.1016\/j.amc.2022.127388","article-title":"Adaptive fixed-time control and synchronization for hyperchaotic L\u00fc systems","volume":"433","author":"Wang","year":"2022","journal-title":"Appl. Math. Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"127115","DOI":"10.1016\/j.amc.2022.127115","article-title":"Chaos synchronization control for stochastic nonlinear systems of interior PMSMs based on fixed-time stability theorem","volume":"430","author":"Tan","year":"2022","journal-title":"Appl. Math. Comput."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/j.matcom.2022.03.010","article-title":"Fixed time control and synchronization of a class of uncertain chaotic systems with disturbances via passive control method","volume":"198","author":"Su","year":"2022","journal-title":"Math. Comput. Simul."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"113609","DOI":"10.1016\/j.chaos.2023.113609","article-title":"Adaptive fixed-time robust control for function projective synchronization of hyperchaotic economic systems with external perturbations","volume":"172","author":"Bekiros","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"122248","DOI":"10.1016\/j.physa.2019.122248","article-title":"Fixed-time projective synchronization of memristive neural networks with discrete delay","volume":"534","author":"Chen","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"113279","DOI":"10.1016\/j.chaos.2023.113279","article-title":"A fixed-time robust controller based on zeroing neural network for generalized projective synchronization of chaotic systems","volume":"169","author":"Xiao","year":"2023","journal-title":"Chao Solitons Fractals"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"16527","DOI":"10.1007\/s00521-024-09885-7","article-title":"Finite-time and fixed-time function projective synchronization of competitive neural networks with noise perturbation","volume":"36","author":"Hao","year":"2024","journal-title":"Neural Comput. Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1049\/iet-cds.2014.0381","article-title":"Generalised mathematical model of memristor","volume":"10","author":"Sun","year":"2016","journal-title":"IET Circuits Devices Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2150035","DOI":"10.1142\/S0217984921500354","article-title":"Generating coexisting attractors from a new four-dimensional chaotic system","volume":"35","author":"Hu","year":"2021","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0375-9601(91)90404-V","article-title":"Numerical methods can suppress chaos","volume":"157","author":"Corless","year":"1991","journal-title":"Phys. Lett. A"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"112794","DOI":"10.1016\/j.chaos.2022.112794","article-title":"Inducing multistability in discrete chaotic systems using numerical integration with variable symmetry","volume":"165","author":"Ostrovskii","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Butusov, D., Karimov, A., Tutueva, A., Kaplun, D., and Nepomuceno, E.G. (2019). The effects of Pad\u00e9 numerical integration in simulation of conservative chaotic systems. Entropy, 21.","DOI":"10.3390\/e21040362"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/j.neunet.2019.12.028","article-title":"A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks","volume":"123","author":"Chen","year":"2020","journal-title":"Neural Netw."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/5\/685\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:24:32Z","timestamp":1760030672000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/5\/685"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,29]]},"references-count":46,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["sym17050685"],"URL":"https:\/\/doi.org\/10.3390\/sym17050685","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,29]]}}}