{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T13:15:35Z","timestamp":1763644535699,"version":"3.37.3"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2025,1,18]],"date-time":"2025-01-18T00:00:00Z","timestamp":1737158400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,18]],"date-time":"2025-01-18T00:00:00Z","timestamp":1737158400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["2021JQ-131","2023-JC-QN-0062","2022JM-013"],"award-info":[{"award-number":["2021JQ-131","2023-JC-QN-0062","2022JM-013"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2025,4]]},"DOI":"10.1007\/s10489-025-06281-z","type":"journal-article","created":{"date-parts":[[2025,1,18]],"date-time":"2025-01-18T06:31:00Z","timestamp":1737181860000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The synchronisation control of fractional 4-D quantum game chaotic map with its application in image encryption"],"prefix":"10.1007","volume":"55","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0663-9887","authenticated-orcid":false,"given":"Zeyu","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Binshuai","family":"Feng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuxin","family":"Yao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xujing","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,1,18]]},"reference":[{"issue":"1","key":"6281_CR1","doi-asserted-by":"publisher","first-page":"218","DOI":"10.28991\/ESJ-2024-08-01-016","volume":"8","author":"W Wydyanto","year":"2024","unstructured":"Wydyanto W, Nayan NM, Sulaiman R, Dewi DA, Kurniawan TB (2024) A hybrid approach to detect and identify text in picture. Emerg Sci J 8(1):218\u2013238. https:\/\/doi.org\/10.28991\/ESJ-2024-08-01-016","journal-title":"Emerg Sci J"},{"key":"6281_CR2","doi-asserted-by":"publisher","first-page":"592","DOI":"10.28991\/ESJ-2024-08-02-014","volume":"8","author":"KW Goh","year":"2024","unstructured":"Goh KW, Surono S, Firza Afitian MY, Mahmudah K, Irsalinda N, Chaimanee M, Choo O (2024) Comparison of activation functions in convolutional neural network for poisson noisy image classification. Emerg Sci J 8:592\u2013602. https:\/\/doi.org\/10.28991\/ESJ-2024-08-02-014","journal-title":"Emerg Sci J"},{"key":"6281_CR3","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.ins.2020.10.048","volume":"550","author":"MZ Talhaoui","year":"2021","unstructured":"Talhaoui MZ, Wang X (2021) A new fractional one dimensional chaotic map and its application in high-speed image encryption. Inf Sci 550:13\u201326. https:\/\/doi.org\/10.1016\/j.ins.2020.10.048","journal-title":"Inf Sci"},{"key":"6281_CR4","doi-asserted-by":"publisher","first-page":"107280","DOI":"10.1016\/j.sigpro.2019.107280","volume":"167","author":"SM Ismail","year":"2020","unstructured":"Ismail SM, Said LA, Radwan AG, Madian AH, Abu-ElYazeed MF (2020) A novel image encryption system merging fractional-order edge detection and generalized chaotic maps. Signal Process 167:107280. https:\/\/doi.org\/10.1016\/j.sigpro.2019.107280","journal-title":"Signal Process"},{"issue":"4","key":"6281_CR5","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1016\/j.optlaseng.2012.11.001","volume":"51","author":"Y Zhang","year":"2013","unstructured":"Zhang Y, Xiao D (2013) Double optical image encryption using discrete Chirikov standard map and chaos-based fractional random transform. Opt Lasers Eng 51(4):472\u2013480. https:\/\/doi.org\/10.1016\/j.optlaseng.2012.11.001","journal-title":"Opt Lasers Eng"},{"issue":"1","key":"6281_CR6","doi-asserted-by":"publisher","first-page":"200","DOI":"10.28991\/HIJ-2024-05-01-015","volume":"5","author":"J Hu","year":"2024","unstructured":"Hu J, Yan Y, Xie Z (2024) Automatic recognition technology of library books based on convolutional neural network model. HighTech Innov J 5(1):200\u2013212. https:\/\/doi.org\/10.28991\/HIJ-2024-05-01-015","journal-title":"HighTech Innov J"},{"issue":"5","key":"6281_CR7","doi-asserted-by":"publisher","first-page":"484","DOI":"10.1016\/j.physleta.2013.12.010","volume":"378","author":"G-C Wu","year":"2014","unstructured":"Wu G-C, Baleanu D, Zeng S-D (2014) Discrete chaos in fractional sine and standard maps. Phys Lett A 378(5):484\u2013487. https:\/\/doi.org\/10.1016\/j.physleta.2013.12.010","journal-title":"Phys Lett A"},{"key":"6281_CR8","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/j.chaos.2018.12.019","volume":"119","author":"A-A Khennaoui","year":"2019","unstructured":"Khennaoui A-A, Ouannas A, Bendoukha S, Grassi G, Lozi RP, Pham V-T (2019) On fractional-order discrete-time systems: Chaos, stabilization and synchronization. Chaos, Solitons Fractals 119:150\u2013162. https:\/\/doi.org\/10.1016\/j.chaos.2018.12.019","journal-title":"Chaos, Solitons Fractals"},{"key":"6281_CR9","doi-asserted-by":"publisher","first-page":"109488","DOI":"10.1016\/j.chaos.2019.109488","volume":"131","author":"L Wang","year":"2020","unstructured":"Wang L, Sun K, Peng Y, He S (2020) Chaos and complexity in a fractional-order higher-dimensional multicavity chaotic map. Chaos, Solitons Fractals 131:109488. https:\/\/doi.org\/10.1016\/j.chaos.2019.109488","journal-title":"Chaos, Solitons Fractals"},{"key":"6281_CR10","doi-asserted-by":"publisher","unstructured":"Sun K, He S, Wang H (2022) Solution and characteristic analysis of fractional-order chaotic systems vol. 1. Springer, Singapore. https:\/\/doi.org\/10.1007\/978-981-19-3273-1","DOI":"10.1007\/978-981-19-3273-1"},{"key":"6281_CR11","doi-asserted-by":"publisher","first-page":"111889","DOI":"10.1016\/j.chaos.2022.111889","volume":"157","author":"S Xu","year":"2022","unstructured":"Xu S, Wang X, Ye X (2022) A new fractional-order chaos system of hopfield neural network and its application in image encryption. Chaos, Solitons Fractals 157:111889. https:\/\/doi.org\/10.1016\/j.chaos.2022.111889","journal-title":"Chaos, Solitons Fractals"},{"issue":"1","key":"6281_CR12","doi-asserted-by":"publisher","first-page":"15737","DOI":"10.1038\/s41598-021-94748-7","volume":"11","author":"X Gao","year":"2021","unstructured":"Gao X, Yu J, Banerjee S, Yan H, Mou J (2021) A new image encryption scheme based on fractional-order hyperchaotic system and multiple image fusion. Sci Rep 11(1):15737. https:\/\/doi.org\/10.1038\/s41598-021-94748-7","journal-title":"Sci Rep"},{"key":"6281_CR13","doi-asserted-by":"publisher","unstructured":"Yang YG, Wang ZJ, Wang BP, Zhou YH, Shi WM, Liao X (2023) A new visually meaningful double-image encryption algorithm combining 2d compressive sensing with fractional-order chaotic system. Multimed Tools Appl 1\u201335. https:\/\/doi.org\/10.1007\/s11042-023-15662-w","DOI":"10.1007\/s11042-023-15662-w"},{"key":"6281_CR14","doi-asserted-by":"publisher","first-page":"1202871","DOI":"10.3389\/fphy.2023.1202871","volume":"11","author":"L Lin","year":"2023","unstructured":"Lin L, Zhuang Y, Xu Z, Yang D, Wu D (2023) Encryption algorithm based on fractional order chaotic system combined with adaptive predefined time synchronization. Front Phys 11:1202871. https:\/\/doi.org\/10.3389\/fphy.2023.1202871","journal-title":"Front Phys"},{"key":"6281_CR15","doi-asserted-by":"publisher","first-page":"114793","DOI":"10.1016\/j.chaos.2024.114793","volume":"182","author":"S Yan","year":"2024","unstructured":"Yan S, Jiang D, Cui Y, Zhang H, Li L (2024) A fractional-order hyperchaotic system that is period in integer-order case and its application in a novel high-quality color image encryption algorithm. Chaos, Solitons Fractals 182:114793. https:\/\/doi.org\/10.1016\/j.chaos.2024.114793","journal-title":"Chaos, Solitons Fractals"},{"key":"6281_CR16","doi-asserted-by":"publisher","unstructured":"Wen H, Lin Y, Kang S, Zhang X, Zou K (2024) Secure image encryption algorithm using chaos-based block permutation and weighted bit planes chain diffusion. IScience 27(1). https:\/\/doi.org\/10.1016\/j.isci.2023.108610","DOI":"10.1016\/j.isci.2023.108610"},{"key":"6281_CR17","doi-asserted-by":"publisher","first-page":"122052","DOI":"10.1016\/j.eswa.2023.122052","volume":"238","author":"NR Zhou","year":"2024","unstructured":"Zhou NR, Hu LL, Huang ZW, Wang MM, Luo GS (2024) Novel multiple color images encryption and decryption scheme based on a bit-level extension algorithm. Expert Syst Appl 238:122052. https:\/\/doi.org\/10.1016\/j.eswa.2023.122052","journal-title":"Expert Syst Appl"},{"key":"6281_CR18","doi-asserted-by":"publisher","unstructured":"Kumari P, Mondal B (2023) Lightweight image encryption algorithm using nlfsr and cbc mode. J Supercomput 1\u201321. https:\/\/doi.org\/10.1007\/s11227-023-05415-9","DOI":"10.1007\/s11227-023-05415-9"},{"issue":"3","key":"6281_CR19","doi-asserted-by":"publisher","first-page":"173804","DOI":"10.1007\/s11227-023-05415-9","volume":"17","author":"X Huang","year":"2023","unstructured":"Huang X, Dong Y, Ye G, Shi Y (2023) Meaningful image encryption algorithm based on compressive sensing and integer wavelet transform. Front Comput Sci 17(3):173804. https:\/\/doi.org\/10.1007\/s11227-023-05415-9","journal-title":"Front Comput Sci"},{"issue":"2","key":"6281_CR20","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/0304-4068(78)90022-8","volume":"5","author":"D Rand","year":"1978","unstructured":"Rand D (1978) Exotic phenomena in games and duopoly models. J Math Econ 5(2):173\u2013184. https:\/\/doi.org\/10.1016\/0304-4068(78)90022-8","journal-title":"J Math Econ"},{"key":"6281_CR21","doi-asserted-by":"publisher","first-page":"1391","DOI":"10.1007\/s11071-015-1950-3","volume":"80","author":"F Wu","year":"2015","unstructured":"Wu F, Ma J (2015) The complex dynamics of a multi-product mixed duopoly model with partial privatization and cross-ownership. Nonlinear Dyn 80:1391\u20131401. https:\/\/doi.org\/10.1007\/s11071-015-1950-3","journal-title":"Nonlinear Dyn"},{"key":"6281_CR22","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1016\/j.amc.2016.09.018","volume":"294","author":"AA Elsadany","year":"2017","unstructured":"Elsadany AA (2017) Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization. Appl Math Comput 294:253\u2013263. https:\/\/doi.org\/10.1016\/j.amc.2016.09.018","journal-title":"Appl Math Comput"},{"key":"6281_CR23","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/j.cnsns.2017.06.015","volume":"58","author":"N Pecora","year":"2018","unstructured":"Pecora N, Sodini M (2018) A heterogenous Cournot duopoly with delay dynamics: Hopf bifurcations and stability switching curves. Commun Nonlinear Sci Numer Simul 58:36\u201346. https:\/\/doi.org\/10.1016\/j.cnsns.2017.06.015","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"6281_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-019-2338-y","volume":"18","author":"L Shi","year":"2019","unstructured":"Shi L, Xu F (2019) Nonlinear dynamics of a quantum Cournot duopoly game with heterogeneous players. Quantum Inf Process 18:1\u201315. https:\/\/doi.org\/10.1007\/s11128-019-2338-y","journal-title":"Quantum Inf Process"},{"key":"6281_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-020-02911-2","volume":"19","author":"X Zhang","year":"2020","unstructured":"Zhang X, Sun D, Jiang W (2020) Dynamics of a heterogeneous quantum Cournot duopoly with adjusting players and quadratic costs. Quantum Inf Process 19:1\u201315. https:\/\/doi.org\/10.1007\/s11128-020-02911-2","journal-title":"Quantum Inf Process"},{"key":"6281_CR26","doi-asserted-by":"publisher","first-page":"133556","DOI":"10.1016\/j.physd.2022.133556","volume":"443","author":"S Wang","year":"2023","unstructured":"Wang S (2023) The synchronization of discrete quantum chaotic maps with uncertainty via compensated control technique. Phys D Nonlinear Phenom 443:133556. https:\/\/doi.org\/10.1016\/j.physd.2022.133556","journal-title":"Phys D Nonlinear Phenom"},{"key":"6281_CR27","doi-asserted-by":"publisher","first-page":"127596","DOI":"10.1016\/j.physa.2022.127596","volume":"600","author":"S-F Wang","year":"2022","unstructured":"Wang S-F (2022) Dynamics, synchronization control of a class of discrete quantum game chaotic map. Phys A Stat Mech Appl 600:127596. https:\/\/doi.org\/10.1016\/j.physa.2022.127596","journal-title":"Phys A Stat Mech Appl"},{"key":"6281_CR28","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1016\/j.cjph.2024.02.012","volume":"90","author":"Z Liu","year":"2024","unstructured":"Liu Z, Feng B, Lu Z, Zhou Y (2024) Fractional-order quantum game chaotic map and its synchronization with application. Chin J Phys 90:1015\u20131025. https:\/\/doi.org\/10.1016\/j.cjph.2024.02.012","journal-title":"Chin J Phys"},{"key":"6281_CR29","doi-asserted-by":"publisher","unstructured":"Owolabi K, Atangana A (2019) Numerical methods for fractional differentiation vol. 1. Springer, Singapore. https:\/\/doi.org\/10.1007\/978-981-15-0098-5","DOI":"10.1007\/978-981-15-0098-5"},{"key":"6281_CR30","doi-asserted-by":"publisher","first-page":"3927","DOI":"10.1140\/epjs\/s11734-021-00323-6","volume":"230","author":"H Fu","year":"2021","unstructured":"Fu H, Wu GC, Yang G, Huang LL (2021) Continuous time random walk to a general fractional Fokker\u2013Planck equation on fractal media. Eur Phys J Spec Top 230:3927\u20133933. https:\/\/doi.org\/10.1140\/epjs\/s11734-021-00323-6","journal-title":"Eur Phys J Spec Top"},{"key":"6281_CR31","doi-asserted-by":"publisher","first-page":"110880","DOI":"10.1016\/j.rser.2021.110880","volume":"144","author":"B Xu","year":"2021","unstructured":"Xu B, Zhang J, Egusquiza M, Chen D, Li F, Behrens P, Egusquiza E (2021) A review of dynamic models and stability analysis for a hydro-turbine governing system. Renew Sustain Energy Rev 144:110880. https:\/\/doi.org\/10.1016\/j.rser.2021.110880","journal-title":"Renew Sustain Energy Rev"},{"key":"6281_CR32","doi-asserted-by":"publisher","first-page":"4596","DOI":"10.1038\/s41598-022-25127-z","volume":"13","author":"M Arif","year":"2023","unstructured":"Arif M, Persio LD, Watthayu PKW, Akg\u00fcl A (2023) Heat transfer analysis of fractional model of couple stress casson tri-hybrid nanofluid using dissimilar shape nanoparticles in blood with biomedical applications. Sci Rep 13:4596. https:\/\/doi.org\/10.1038\/s41598-022-25127-z","journal-title":"Sci Rep"},{"key":"6281_CR33","doi-asserted-by":"publisher","unstructured":"Ren G, Yu Y, Lu Z, Chen W (2021) A fractional order model for rumor spreading in mobile social networks from a stochastic process. In: 2021 9th International Conference on Systems and Control (ICSC). IEEE, pp 312\u2013318. https:\/\/doi.org\/10.1109\/ICSC50472.2021.9666673","DOI":"10.1109\/ICSC50472.2021.9666673"},{"key":"6281_CR34","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1016\/j.aej.2022.09.033","volume":"65","author":"Q Chen","year":"2023","unstructured":"Chen Q, Sabir Z, Raja MAZ, Gao W, Baskonus HM (2023) A fractional study based on the economic and environmental mathematical model. Alex Eng J 65:761\u2013770. https:\/\/doi.org\/10.1016\/j.aej.2022.09.033","journal-title":"Alex Eng J"},{"key":"6281_CR35","doi-asserted-by":"publisher","first-page":"100470","DOI":"10.1016\/j.padiff.2022.100470","volume":"7","author":"SL Khalaf","year":"2023","unstructured":"Khalaf SL, Kadhim MS, Khudair AR (2023) Studying of covid-19 fractional model: Stability analysis. Partial Differ Equ Appl Math 7:100470. https:\/\/doi.org\/10.1016\/j.padiff.2022.100470","journal-title":"Partial Differ Equ Appl Math"},{"issue":"3","key":"6281_CR36","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s11082-022-04488-9","volume":"55","author":"MI Asjad","year":"2023","unstructured":"Asjad MI, Inc M, Faridi WA, Bakar MA, Muhammad T, Rezazadeh H (2023) Optical solitonic structures with singular and non-singular 25 kernel for nonlinear fractional model in quantum mechanics. Opt Quantum Electron 55(3):219. https:\/\/doi.org\/10.1007\/s11082-022-04488-9","journal-title":"Opt Quantum Electron"},{"key":"6281_CR37","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1016\/j.matcom.2021.12.009","volume":"194","author":"J Shi","year":"2022","unstructured":"Shi J, He K, Fang H (2022) Chaos, hopf bifurcation and control of a fractional-order delay financial system. Math Comput Simul 194:348\u2013364. https:\/\/doi.org\/10.1016\/j.matcom.2021.12.009","journal-title":"Math Comput Simul"},{"key":"6281_CR38","doi-asserted-by":"publisher","first-page":"112633","DOI":"10.1016\/j.cam.2019.112633","volume":"370","author":"LL Huang","year":"2020","unstructured":"Huang LL, Park JH, Wu GC, Mo ZW (2020) Variable-order fractional discrete-time recurrent neural networks. J Comput Appl Math 370:112633. https:\/\/doi.org\/10.1016\/j.cam.2019.112633","journal-title":"J Comput Appl Math"},{"issue":"1","key":"6281_CR39","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1515\/fca-2019-0012","volume":"22","author":"GC Wu","year":"2019","unstructured":"Wu GC, Zeng DQ, Baleanu D (2019) Fractional impulsive differential equations: exact solutions, integral equations and short memory case. Fractional Calc Appl Anal 22(1):180\u2013192. https:\/\/doi.org\/10.1515\/fca-2019-0012","journal-title":"Fractional Calc Appl Anal"},{"issue":"03","key":"6281_CR40","doi-asserted-by":"publisher","first-page":"2150064","DOI":"10.1142\/S0218348X2150064X","volume":"29","author":"Z Liu","year":"2021","unstructured":"Liu Z, Xia T, Wang Y (2021) Image encryption technology based on fractional two dimensional discrete chaotic map accompanied with menezes-vanstone elliptic curve cryptosystem. Fractals 29(03):2150064. https:\/\/doi.org\/10.1142\/S0218348X2150064X","journal-title":"Fractals"},{"key":"6281_CR41","first-page":"165","volume":"2","author":"FM Atici","year":"2007","unstructured":"Atici FM, Eloe PW (2007) A transform method in discrete fractional calculus. Int J Diff Equ 2:165\u2013176","journal-title":"Int J Diff Equ"},{"key":"6281_CR42","first-page":"574","volume":"13","author":"T Abdeljawad","year":"2011","unstructured":"Abdeljawad T, Baleanu D (2011) Fractional differences and integration by parts. J Comput Anal Appl 13:574\u2013582","journal-title":"J Comput Anal Appl"},{"key":"6281_CR43","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/j.sigpro.2014.02.022","volume":"102","author":"GC Wu","year":"2014","unstructured":"Wu GC, Baleanu D (2014) Chaos synchronization of the discrete fractional logistic map. Signal Process 102:96\u201399. https:\/\/doi.org\/10.1016\/j.sigpro.2014.02.022","journal-title":"Signal Process"},{"key":"6281_CR44","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2011\/713201","volume":"1","author":"F Chen","year":"2011","unstructured":"Chen F, Luo X, Zhou Y (2011) Existence results for nonlinear fractional difference equation. Adv Diff Equ 1:1\u201312. https:\/\/doi.org\/10.1155\/2011\/713201","journal-title":"Adv Diff Equ"},{"key":"6281_CR45","doi-asserted-by":"publisher","unstructured":"Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821. https:\/\/doi.org\/10.1103\/PhysRevLett.64.821","DOI":"10.1103\/PhysRevLett.64.821"},{"issue":"3","key":"6281_CR46","doi-asserted-by":"publisher","first-page":"613","DOI":"10.2478\/s13540-013-0039-2","volume":"16","author":"R Abu-Saris","year":"2013","unstructured":"Abu-Saris R, Al-Mdallal Q (2013) On the asymptotic stability of linear system of fractional-order difference equations. Fractional Calc Appl Anal 16(3):613\u2013629. https:\/\/doi.org\/10.2478\/s13540-013-0039-2","journal-title":"Fractional Calc Appl Anal"},{"key":"6281_CR47","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.cnsns.2014.06.042","volume":"1\u20133","author":"GC Wu","year":"2015","unstructured":"Wu GC, Baleanu D (2015) Jacobian matrix algorithm for lyapunov exponents of the discrete fractional maps. Commun Nonlinear Sci Numer Simul 1\u20133:95\u2013100. https:\/\/doi.org\/10.1016\/j.cnsns.2014.06.042","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"6281_CR48","doi-asserted-by":"publisher","first-page":"2129","DOI":"10.1142\/S0218127406015970","volume":"16","author":"G Alvarez","year":"2006","unstructured":"Alvarez G, Li S (2006) Some basic cryptographic requirements for chaos-based cryptosystems. Int J Bifurcation Chaos 16:2129\u20132151. https:\/\/doi.org\/10.1142\/S0218127406015970","journal-title":"Int J Bifurcation Chaos"},{"key":"6281_CR49","doi-asserted-by":"publisher","first-page":"75834","DOI":"10.1109\/ACCESS.2018.2883690","volume":"6","author":"C Li","year":"2018","unstructured":"Li C, Lin D, Feng B, Lv J, Hao F (2018) Cryptanalysis of a chaotic image encryption algorithm based on information entropy. IEEE Access 6:75834\u201375842. https:\/\/doi.org\/10.1109\/ACCESS.2018.2883690","journal-title":"IEEE Access"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-025-06281-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10489-025-06281-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-025-06281-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T17:22:31Z","timestamp":1740244951000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10489-025-06281-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,18]]},"references-count":49,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["6281"],"URL":"https:\/\/doi.org\/10.1007\/s10489-025-06281-z","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"type":"print","value":"0924-669X"},{"type":"electronic","value":"1573-7497"}],"subject":[],"published":{"date-parts":[[2025,1,18]]},"assertion":[{"value":"9 January 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 January 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical and informed consent for data used"}},{"value":"The authors of this work report no potential conflicts of interest.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"343"}}