{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:32:33Z","timestamp":1773815553052,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T00:00:00Z","timestamp":1661299200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Heilongjiang Province of China","award":["YQ2020F012"],"award-info":[{"award-number":["YQ2020F012"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Considering the security of a communication system, designing a high-dimensional complex chaotic system suitable for chaotic synchronization has become a key problem in chaotic secure communication. In this paper, a new 5-D hyperchaotic system with high order nonlinear terms was constructed and proved to be hyperchaotic by dynamical characterization characteristics, the maximum Lyapunov exponent was close to 2, and there was a better permutation entropy index, while a valid chaotic sequence could be generated in three cycles in the FPGA (Field Programmable Gate Array)-based implementation. A multivariable nonlinear feedback synchronous controller based on FPGA was proposed to design and implement synchronization of high order complex hyperchaotic systems. The results show that the error signal converged to 0 rapidly under the effect of the nonlinear feedback synchronous controller. This lays the foundation for the synchronization of high order complex chaotic systems.<\/jats:p>","DOI":"10.3390\/e24091179","type":"journal-article","created":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T21:03:51Z","timestamp":1661375031000},"page":"1179","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["FPGA-Based Implementation and Synchronization Design of a New Five-Dimensional Hyperchaotic System"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4581-7706","authenticated-orcid":false,"given":"Ya","family":"Wang","sequence":"first","affiliation":[{"name":"Electronic Engineering College, Heilongjiang University, Harbin 150080, China"}]},{"given":"Xinyu","family":"Li","sequence":"additional","affiliation":[{"name":"Electronic Engineering College, Heilongjiang University, Harbin 150080, China"}]},{"given":"Xiaodong","family":"Li","sequence":"additional","affiliation":[{"name":"Beijing Aerospace Institute of Automatic Control, Beijing 100854, China"}]},{"given":"Yerui","family":"Guang","sequence":"additional","affiliation":[{"name":"Electronic Engineering College, Heilongjiang University, Harbin 150080, China"}]},{"given":"Yanan","family":"Wu","sequence":"additional","affiliation":[{"name":"Electronic Engineering College, Heilongjiang University, Harbin 150080, China"}]},{"given":"Qun","family":"Ding","sequence":"additional","affiliation":[{"name":"Electronic Engineering College, Heilongjiang University, Harbin 150080, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","article-title":"Deterministic Nonperiodic Flow","volume":"20","author":"Lorenz","year":"1963","journal-title":"J. Atmos. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1140\/epjst\/e2020-900225-9","article-title":"Extreme multi-stability analysis of a novel 5D chaotic system with hidden attractors, line equilibrium, permutation entropy and its secure communication scheme","volume":"229","author":"Khalaf","year":"2020","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6168562","DOI":"10.1155\/2021\/6168562","article-title":"Application of CNN Algorithm Based on Chaotic Recursive Diagonal Model in Medical Image Processing","volume":"2021","author":"Ye","year":"2021","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"36667","DOI":"10.1109\/ACCESS.2019.2906292","article-title":"Novel Medical Image Encryption Scheme Based on Chaos and DNA Encoding","volume":"7","author":"Belazi","year":"2019","journal-title":"IEEE Access"},{"key":"ref_5","first-page":"1","article-title":"Medical Image Encryption using Chaotic Map Improved Advanced Encryption Standard","volume":"10","author":"Bhogal","year":"2018","journal-title":"Int. J. Inf. Technol. Comput. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Liao, T., Chen, H., Peng, C.Y., and Hou, Y.Y. (2021). Chaos-Based Secure Communications in Biomedical Information Application. Electronics, 10.","DOI":"10.3390\/electronics10030359"},{"key":"ref_7","unstructured":"(2020). Biotechnology. Biomedical Engineering. Reports Summarize Biomedical Engineering Findings from Kiet Group Institute (R-Peak Detection Using Chaos Analysis in Standard and Real Time ECG Databases), Biotech Week."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"181","DOI":"10.3390\/e17010181","article-title":"An Image Encryption Scheme Based on Hyperchaotic Rabinovich and Exponential Chaos Maps","volume":"17","author":"Tong","year":"2015","journal-title":"Entropy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1750185","DOI":"10.1142\/S0218127417501851","article-title":"Bifurcations and Chaos for 2D Discontinuous Dynamical Model of Financial Markets","volume":"27","author":"Gu","year":"2017","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1504\/IJNDC.2019.098682","article-title":"Chaotic financial system with uncertain parameters-its control and synchronisation","volume":"1","author":"Idowu","year":"2019","journal-title":"Int. J. Nonlinear Dyn. Control"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"52896","DOI":"10.1109\/ACCESS.2019.2911486","article-title":"Dynamic Analysis and Finite-Time Synchronization of a New Hyperchaotic System With Coexisting Attractors","volume":"7","author":"Zhou","year":"2019","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Li, S., Wu, Y., and Zhang, X. (2021). Analysis and Synchronization of a New Hyperchaotic System with Exponential Term. Mathematics, 9.","DOI":"10.3390\/math9243281"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1504\/IJCAT.2020.111848","article-title":"FPGA design and circuit implementation of a new four-dimensional multistable hyperchaotic system with coexisting attractors","volume":"64","author":"Vaidyanathan","year":"2020","journal-title":"Int. J. Comput. Appl. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2150280","DOI":"10.1142\/S0218126621502807","article-title":"Design and FPGA Implementation of New Multidimensional Chaotic Map for Secure Communication","volume":"30","author":"Belqassim","year":"2021","journal-title":"J. Circuits Syst. Comput."},{"key":"ref_15","first-page":"323","article-title":"Chen-like system design and its FPGA implementation","volume":"39","author":"Yuan","year":"2015","journal-title":"J. Nanjing Univ. Sci. Technol."},{"key":"ref_16","first-page":"113","article-title":"FPGA design and implementation of super chaotic video encryption system","volume":"58","author":"Liu","year":"2018","journal-title":"Telecommun. Technol."},{"key":"ref_17","first-page":"7","article-title":"FPGA design and implementation of chaotic pseudo-random sequence generator","volume":"31","author":"Sun","year":"2014","journal-title":"Comput. Appl. Softw."},{"key":"ref_18","first-page":"1","article-title":"FPGA-based synchronization of four-wing hyperchaotic systems and their confidential video communication","volume":"49","author":"Xue","year":"2019","journal-title":"J. Shandong Univ."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Tang, X., Zhen, J., and Ding, Q. (2019). Chaos Synchronization and Voice Encryption of Discretized Hyperchaotic Chen Based on Euler Algorithm. International Conference in Communications, Signal Processing, and Systems, Springer.","DOI":"10.1007\/978-981-13-9409-6_189"},{"key":"ref_20","unstructured":"Liu, H. (2014). Research on Chaotic Synchronization and Its Application in Image Encryption, Northeastern University."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"109542","DOI":"10.1016\/j.measurement.2021.109542","article-title":"Robust observer-based adaptive synchronization control of uncertain nonlinear bilateral teleoperation systems under time-varying delay","volume":"182","author":"Mehrjouyan","year":"2021","journal-title":"Measurement"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"9936224","DOI":"10.1155\/2021\/9936224","article-title":"Optimal Adaptive Control and Backstepping Control Method with Sliding Mode Differentiator","volume":"2021","author":"Sun","year":"2021","journal-title":"Complexity"},{"key":"ref_23","unstructured":"Huang, Y. (2021). Drive-Response Shape Asymptotic Synchronous Control of Chaotic Systems and Its Application, Guangdong University of Technology."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4903","DOI":"10.1166\/jctn.2019.8540","article-title":"Synchronization of Liu-Su-Liu and Liu-Chen-Liu Chaotic Systems by Nonlinear Feedback Control","volume":"16","author":"Regan","year":"2019","journal-title":"J. Comput. Theor. Nanosci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"105708","DOI":"10.1016\/j.cnsns.2021.105708","article-title":"Chaos synchronization in generalized Lorenz systems and an application to image encryption","volume":"96","author":"Moon","year":"2021","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1076","DOI":"10.4028\/www.scientific.net\/AMM.635-637.1076","article-title":"Achieving the Multi-Scroll Chaotic Attractors\u2019 Synchronization in the Four-Dimensional System by Driving-Response Synchronization Method","volume":"3485","author":"Li","year":"2014","journal-title":"Appl. Mech. Mater."},{"key":"ref_27","first-page":"235","article-title":"New four-dimensional hyperchaotic Liou systems and their chaotic synchronization","volume":"296","author":"Liu","year":"2013","journal-title":"J. Univ. Electron. Sci. Technol."},{"key":"ref_28","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_29","doi-asserted-by":"crossref","unstructured":"Vaidyanathan, S., Tlelo-Cuautle, E., Guill\u00e9n-Fern\u00e1ndez, O., Benkouider, K., and Sambas, A. (2022). A New 4-D Hyperchaotic System with No Balance Point, Its Bifurcation Analysis, Multi-Stability, Circuit Simulation, and FPGA Realization. Complex Systems and Their Applications, Springer.","DOI":"10.1007\/978-3-031-02472-6_9"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Ding, L., and Ding, Q. (2020). The Establishment and Dynamic Properties of a New 4D Hyperchaotic System with Its Application and Statistical Tests in Gray Images. Entropy, 22.","DOI":"10.3390\/e22030310"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/9\/1179\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:14:37Z","timestamp":1760141677000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/9\/1179"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,24]]},"references-count":30,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["e24091179"],"URL":"https:\/\/doi.org\/10.3390\/e24091179","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,24]]}}}