{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T13:04:43Z","timestamp":1784898283106,"version":"3.55.0"},"reference-count":44,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"funder":[{"DOI":"10.13039\/501100021171","name":"Basic and Applied Basic Research Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2024A1515011910"],"award-info":[{"award-number":["2024A1515011910"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62571183"],"award-info":[{"award-number":["62571183"]}],"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":["62271197"],"award-info":[{"award-number":["62271197"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematics and Computers in Simulation"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.matcom.2026.06.003","type":"journal-article","created":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T05:42:37Z","timestamp":1780897357000},"page":"727-743","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["A discrete memristive heterogeneous neural network with grid multi-windmill hyperchaotic attractors and application in secure communication"],"prefix":"10.1016","volume":"249","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6654-7349","authenticated-orcid":false,"given":"Gang","family":"Yang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6522-9795","authenticated-orcid":false,"given":"Chunhua","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yichuang","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4015-5280","authenticated-orcid":false,"given":"Quanli","family":"Deng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"12","key":"10.1016\/j.matcom.2026.06.003_b1","doi-asserted-by":"crossref","first-page":"4701","DOI":"10.1109\/TCAD.2025.3567534","article-title":"Memristor-based brain emotional learning neural network with attention mechanism and its application","volume":"44","author":"Deng","year":"2025","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."},{"issue":"4","key":"10.1016\/j.matcom.2026.06.003_b2","doi-asserted-by":"crossref","first-page":"2737","DOI":"10.1109\/TCSI.2025.3623472","article-title":"A universal framework for configuring fully mem-element-based bionic spiking circuits","volume":"73","author":"Xu","year":"2025","journal-title":"IEEE Trans. Circuits Syst. I. Regul. Pap."},{"key":"10.1016\/j.matcom.2026.06.003_b3","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2025.116587","article-title":"Firing activities induced by various stimuli in a memristive ion channel-based bionic circuit","volume":"199","author":"Ding","year":"2025","journal-title":"Chaos Solitons Fractals"},{"issue":"6","key":"10.1016\/j.matcom.2026.06.003_b4","doi-asserted-by":"crossref","first-page":"2271","DOI":"10.1109\/TCSI.2023.3250699","article-title":"Modeling and analysis of spike signal sequence for memristor crossbar array in neuromorphic chips","volume":"70","author":"Tao","year":"2023","journal-title":"IEEE Trans. Circuits Syst. I. Regul. Pap."},{"key":"10.1016\/j.matcom.2026.06.003_b5","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.matcom.2025.04.005","article-title":"Complex dynamics and encryption application of a 3D dual-memristor oscillatory hyperchaotic map","volume":"236","author":"Lai","year":"2025","journal-title":"Math. Comput. Simulation"},{"key":"10.1016\/j.matcom.2026.06.003_b6","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.matcom.2025.01.022","article-title":"Excitability and synchronization of vanadium dioxide memristor-inspired neurons","volume":"233","author":"Shao","year":"2025","journal-title":"Math. Comput. Simulation"},{"key":"10.1016\/j.matcom.2026.06.003_b7","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2024.115740","article-title":"A memristive Ikeda map and its application in image encryption","volume":"190","author":"Wang","year":"2025","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2026.06.003_b8","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2025.117823","article-title":"Hidden dynamical transitions and firing patterns in a memristive Wilson circuit","volume":"205","author":"Xu","year":"2026","journal-title":"Chaos Solitons Fractals"},{"issue":"19","key":"10.1016\/j.matcom.2026.06.003_b9","doi-asserted-by":"crossref","first-page":"40934","DOI":"10.1109\/JIOT.2025.3590465","article-title":"A unified framework for generating 4D discrete memristive hyperchaotic maps with complex dynamics and application to encryption","volume":"12","author":"Lai","year":"2025","journal-title":"IEEE Internet Things J."},{"issue":"8","key":"10.1016\/j.matcom.2026.06.003_b10","doi-asserted-by":"crossref","first-page":"7706","DOI":"10.1109\/TCSVT.2025.3545868","article-title":"A 3D memristive cubic map with dual discrete memristors: design, implementation, and application in image encryption","volume":"35","author":"Gao","year":"2025","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"issue":"3","key":"10.1016\/j.matcom.2026.06.003_b11","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1109\/TCSI.2023.3347411","article-title":"Spatiotemporal chaos in a sine map lattice with discrete memristor coupling","volume":"71","author":"He","year":"2024","journal-title":"IEEE Trans. Circuits Syst. I. Regul. Pap."},{"issue":"12","key":"10.1016\/j.matcom.2026.06.003_b12","doi-asserted-by":"crossref","first-page":"7993","DOI":"10.1109\/TCSI.2025.3571961","article-title":"Delay difference feedback memristive map: Dynamics, hardware implementation, and application in path planning","volume":"72","author":"Deng","year":"2025","journal-title":"IEEE Trans. Circuits Syst. I. Regul. Pap."},{"issue":"20","key":"10.1016\/j.matcom.2026.06.003_b13","doi-asserted-by":"crossref","first-page":"28381","DOI":"10.1007\/s11071-025-11556-8","article-title":"Discrete memristive hyperchaotic maps with high Lyapunov exponents","volume":"113","author":"Luo","year":"2025","journal-title":"Nonlinear Dynam."},{"key":"10.1016\/j.matcom.2026.06.003_b14","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.matcom.2022.04.005","article-title":"Segmented disc dynamo with symmetric multidirectional patterns of multiscroll chaotic attractors","volume":"200","author":"Azam","year":"2022","journal-title":"Math. Comput. Simulation"},{"issue":"12","key":"10.1016\/j.matcom.2026.06.003_b15","doi-asserted-by":"crossref","DOI":"10.1088\/1674-1056\/adfeff","article-title":"Multi-scroll Hopfield neural network excited by memristive self-synapses and its application in image encryption","volume":"34","author":"He","year":"2025","journal-title":"Chin. Phys. B"},{"issue":"7","key":"10.1016\/j.matcom.2026.06.003_b16","doi-asserted-by":"crossref","first-page":"4039","DOI":"10.1109\/TCYB.2024.3377011","article-title":"Constructing multiscroll memristive neural network with local activity memristor and application in image encryption","volume":"54","author":"Lai","year":"2024","journal-title":"IEEE Trans. Cybern."},{"issue":"10","key":"10.1016\/j.matcom.2026.06.003_b17","doi-asserted-by":"crossref","first-page":"7824","DOI":"10.1109\/TNNLS.2022.3146570","article-title":"Design and analysis of multiscroll memristive Hopfield neural network with adjustable memductance and application to image encryption","volume":"34","author":"Lai","year":"2022","journal-title":"IEEE Trans. Neural Networks Learn. Syst."},{"key":"10.1016\/j.matcom.2026.06.003_b18","doi-asserted-by":"crossref","DOI":"10.1109\/TCAD.2026.3661893","article-title":"A discrete memristive Hopfield neural network with grid multi-structure\/scroll-like attractors","author":"Yang","year":"2026","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."},{"issue":"8","key":"10.1016\/j.matcom.2026.06.003_b19","doi-asserted-by":"crossref","first-page":"3764","DOI":"10.1109\/TCSI.2024.3412806","article-title":"A universal discrete memristor with application to multi-attractor generation","volume":"71","author":"Zhang","year":"2024","journal-title":"IEEE Trans. Circuits Syst. I. Regul. Pap."},{"issue":"12","key":"10.1016\/j.matcom.2026.06.003_b20","doi-asserted-by":"crossref","first-page":"20902","DOI":"10.1109\/JIOT.2025.3545369","article-title":"Discrete memristive Hopfield neural network with multi-stripe\/wave hyperchaos","volume":"12","author":"Bao","year":"2025","journal-title":"IEEE Internet Things J."},{"key":"10.1016\/j.matcom.2026.06.003_b21","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2024.115070","article-title":"Dynamics analysis and feasibility verification of a 3D discrete memristive chaotic map with multi-vortex-like volume behavior","volume":"185","author":"Fan","year":"2024","journal-title":"Chaos Solitons Fractals"},{"issue":"7","key":"10.1016\/j.matcom.2026.06.003_b22","doi-asserted-by":"crossref","first-page":"9082","DOI":"10.1109\/JIOT.2024.3506118","article-title":"Novel n-dimensional non-degenerate discrete hyperchaotic map with any desired Lyapunov exponents","volume":"12","author":"Zhou","year":"2024","journal-title":"IEEE Internet Things J."},{"issue":"10","key":"10.1016\/j.matcom.2026.06.003_b23","doi-asserted-by":"crossref","first-page":"6516","DOI":"10.1109\/TSMC.2023.3283433","article-title":"Generation of n-dimensional hyperchaotic maps using gershgorin-type theorem and its application","volume":"53","author":"Zhang","year":"2023","journal-title":"IEEE Trans. Syst. Man, Cybern.: Syst."},{"issue":"6","key":"10.1016\/j.matcom.2026.06.003_b24","doi-asserted-by":"crossref","first-page":"6412","DOI":"10.1109\/TIE.2024.3497320","article-title":"N-dimensional hyperchaotic discrete maps with desired positive Lyapunov exponents and its application in secure communication","volume":"72","author":"Tang","year":"2024","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"3","key":"10.1016\/j.matcom.2026.06.003_b25","doi-asserted-by":"crossref","first-page":"247","DOI":"10.31887\/DCNS.2013.15.3\/osporns","article-title":"Structure and function of complex brain networks","volume":"15","author":"Sporns","year":"2013","journal-title":"Dialogues Clin. Neurosci."},{"issue":"3","key":"10.1016\/j.matcom.2026.06.003_b26","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1038\/nn.4502","article-title":"Network neuroscience","volume":"20","author":"Bassett","year":"2017","journal-title":"Nature Neurosci."},{"key":"10.1016\/j.matcom.2026.06.003_b27","doi-asserted-by":"crossref","first-page":"29983","DOI":"10.1007\/s11071-025-11603-4","article-title":"Memristor coupled fractional-order Hopfield neural network composed by heterogeneous neurons and its FPGA implementation","volume":"113","author":"Luo","year":"2025","journal-title":"Nonlinear Dynam."},{"issue":"5","key":"10.1016\/j.matcom.2026.06.003_b28","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1007\/s11071-026-12216-1","article-title":"Bursting generation and synchronization mechanisms of a heterogeneous neuronal network with memristor synapse","volume":"114","author":"Tong","year":"2026","journal-title":"Nonlinear Dynam."},{"issue":"4","key":"10.1016\/j.matcom.2026.06.003_b29","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s11071-025-12152-6","article-title":"Heterogeneous whole-brain neural network constructed by SW-SW architecture and PLV matrix","volume":"114","author":"Ma","year":"2026","journal-title":"Nonlinear Dynam."},{"issue":"4","key":"10.1016\/j.matcom.2026.06.003_b30","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s11071-025-12127-7","article-title":"A discrete memristive heterogeneous Hopfield neural network with multi-penguin-like\/silkworm-like attractors and its application in secure communication","volume":"114","author":"Yang","year":"2026","journal-title":"Nonlinear Dynam."},{"issue":"12","key":"10.1016\/j.matcom.2026.06.003_b31","doi-asserted-by":"crossref","first-page":"7333","DOI":"10.1109\/TCYB.2024.3471644","article-title":"An FHN-HR neuron network coupled with a novel locally active memristor and its DSP implementation","volume":"54","author":"Mou","year":"2024","journal-title":"IEEE Trans. Cybern."},{"key":"10.1016\/j.matcom.2026.06.003_b32","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2024.114466","article-title":"A discrete Chialvo-Rulkov neuron network coupled with a novel memristor model: Design, dynamical analysis, DSP implementation and its application","volume":"179","author":"Cao","year":"2024","journal-title":"Chaos Solitons Fractals"},{"issue":"12","key":"10.1016\/j.matcom.2026.06.003_b33","doi-asserted-by":"crossref","DOI":"10.1088\/1674-1056\/ae0a3b","article-title":"Discrete neuron models and memristive neural network mapping: A comprehensive review","volume":"34","author":"Yu","year":"2025","journal-title":"Chin. Phys. B"},{"issue":"11","key":"10.1016\/j.matcom.2026.06.003_b34","doi-asserted-by":"crossref","first-page":"3458","DOI":"10.1109\/TNNLS.2019.2892385","article-title":"Memristive imitation of synaptic transmission and plasticity","volume":"30","author":"Mannan","year":"2019","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"10.1016\/j.matcom.2026.06.003_b35","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2024.115191","article-title":"Collective dynamics of adaptive memristor synapse-cascaded neural networks based on energy flow","volume":"186","author":"Zhang","year":"2024","journal-title":"Chaos Solitons Fractals"},{"issue":"6","key":"10.1016\/j.matcom.2026.06.003_b36","doi-asserted-by":"crossref","first-page":"11425","DOI":"10.1109\/JIOT.2025.3646638","article-title":"Delayed discrete memristive ring neural network and application in pseudorandom number generator","volume":"13","author":"Yang","year":"2025","journal-title":"IEEE Internet Things J."},{"issue":"12","key":"10.1016\/j.matcom.2026.06.003_b37","doi-asserted-by":"crossref","first-page":"887","DOI":"10.3390\/fractalfract7120887","article-title":"Exploiting newly designed fractional-order 3D Lorenz chaotic system and 2D discrete polynomial hyper-chaotic map for high-performance multi-image encryption","volume":"7","author":"Feng","year":"2023","journal-title":"Fractal Fract."},{"issue":"22","key":"10.1016\/j.matcom.2026.06.003_b38","doi-asserted-by":"crossref","first-page":"20417","DOI":"10.1007\/s11071-024-10099-8","article-title":"A new image encryption algorithm with feedback key mechanism using two-dimensional dual discrete quadratic chaotic map","volume":"112","author":"Yin","year":"2024","journal-title":"Nonlinear Dynam."},{"issue":"3","key":"10.1016\/j.matcom.2026.06.003_b39","doi-asserted-by":"crossref","first-page":"2867","DOI":"10.1007\/s11071-024-10331-5","article-title":"A novel 2D Log-Logistic-Sine chaotic map for image encryption","volume":"113","author":"Wang","year":"2025","journal-title":"Nonlinear Dynam."},{"issue":"1","key":"10.1016\/j.matcom.2026.06.003_b40","doi-asserted-by":"crossref","DOI":"10.7498\/aps.75.20251242","article-title":"Discrete memristor-based complex-valued chaotic system dynamic analysis and its application in dual-image encryption","volume":"75","author":"Deng","year":"2026","journal-title":"Acta Phys. Sin."},{"key":"10.1016\/j.matcom.2026.06.003_b41","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.matcom.2025.06.009","article-title":"Color image encryption scheme based on a novel 2D-CLCM chaotic system and RNA encoding","volume":"239","author":"Liu","year":"2025","journal-title":"Math. Comput. Simulation"},{"key":"10.1016\/j.matcom.2026.06.003_b42","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.matcom.2022.12.025","article-title":"Secure image encryption scheme based on a new robust chaotic map and strong S-box","volume":"207","author":"Zhu","year":"2023","journal-title":"Math. Comput. Simulation"},{"issue":"6","key":"10.1016\/j.matcom.2026.06.003_b43","doi-asserted-by":"crossref","first-page":"5298","DOI":"10.1109\/TII.2026.3663427","article-title":"A class of discrete memristive hyperchaotic maps with multicavity multistructure attractors and its application in secure communication","volume":"22","author":"Yang","year":"2026","journal-title":"IEEE Trans. Ind. Inform."},{"issue":"2","key":"10.1016\/j.matcom.2026.06.003_b44","first-page":"31","article-title":"NPCR and UACI randomness tests for image encryption","volume":"1","author":"Wu","year":"2011","journal-title":"Cyber J.: Multidiscip. J. Sci. Technol. J. Sel. Areas Telecommun. (JSAT)"}],"container-title":["Mathematics and Computers in Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426002466?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426002466?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T12:36:55Z","timestamp":1784896615000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0378475426002466"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":44,"alternative-id":["S0378475426002466"],"URL":"https:\/\/doi.org\/10.1016\/j.matcom.2026.06.003","relation":{},"ISSN":["0378-4754"],"issn-type":[{"value":"0378-4754","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A discrete memristive heterogeneous neural network with grid multi-windmill hyperchaotic attractors and application in secure communication","name":"articletitle","label":"Article Title"},{"value":"Mathematics and Computers in Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.matcom.2026.06.003","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}]}}