{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T10:24:04Z","timestamp":1770459844201,"version":"3.49.0"},"reference-count":69,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2022,5,16]],"date-time":"2022-05-16T00:00:00Z","timestamp":1652659200000},"content-version":"vor","delay-in-days":135,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"name":"Chennai Institute of Technology, India","award":["CIT\/CNS\/2021\/RD\/064"],"award-info":[{"award-number":["CIT\/CNS\/2021\/RD\/064"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:p>This paper is reporting on electronic implementation of a three\u2010dimensional autonomous system with infinite equilibrium point belonging to a parabola. Performance analysis of an adaptive synchronization via relay coupling and a hybrid steganography chaos encryption application are provided. Besides striking parabolic equilibrium, the proposed three\u2010dimensional autonomous system also exhibits hidden chaotic oscillations as well as hidden chaotic bursting oscillations. Electronic implementation of the hidden chaotic behaviors is done to confirm their physical existence. A good qualitative agreement is shown between numerical simulations and OrCAD\u2010PSpice results. Moreover, adaptive synchronization via relay coupling of three three\u2010dimensional autonomous systems with a parabolic equilibrium is analysed by using time histories. Numerical results demonstrate that global synchronization is achieved between the three units. Finally, chaotic behavior found is exploited to provide a suitable text encryption scheme by hidden secret message inside an image using steganography and chaos encryption.<\/jats:p>","DOI":"10.1155\/2022\/8362836","type":"journal-article","created":{"date-parts":[[2022,5,16]],"date-time":"2022-05-16T18:50:09Z","timestamp":1652727009000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Three\u2010Dimensional Autonomous System with a Parabolic Equilibrium: Dynamical Analysis, Adaptive Synchronization via Relay Coupling, and Applications to Steganography and Chaos Encryption"],"prefix":"10.1155","volume":"2022","author":[{"given":"Janarthanan","family":"Ramadoss","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9833-4014","authenticated-orcid":false,"given":"Romanic","family":"Kengne","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dianorr\u00e9","family":"Tokoue Ngatcha","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Victor","family":"Kamdoum Tamba","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2993-7182","authenticated-orcid":false,"given":"Karthikeyan","family":"Rajagopal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marceline","family":"Motchongom Tingue","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,5,16]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1142\/7183"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2011.04.037"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2012.05.016"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127413300024"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-014-1292-6"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2015.04.007"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40435-019-00531-y"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2019.01.015"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2016.05.002"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127421300147"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127413501885"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1142\/s021812741450134x"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/i2014-14076-4"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127414500102"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127414501466"},{"key":"e_1_2_9_16_2","first-page":"535","article-title":"Generating a novel hyperchaotic system out of equilibrium","volume":"8","author":"Pham V.-T.","year":"2014","journal-title":"Optoelectronics and Advanced Materials-Rapid Communications"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjst\/e2015-02472-1"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjst\/e2015-02485-8"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2015.06.039"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127416502114"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127416500310"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1142\/s021812741650098x"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127416500693"},{"key":"e_1_2_9_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2011.10.040"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-012-0669-7"},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.04.011"},{"key":"e_1_2_9_27_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127416502254"},{"key":"e_1_2_9_28_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218126618500664"},{"key":"e_1_2_9_29_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127414500874"},{"key":"e_1_2_9_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2016.10.002"},{"key":"e_1_2_9_31_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127417501309"},{"key":"e_1_2_9_32_2","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/7871467"},{"key":"e_1_2_9_33_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3556-4"},{"key":"e_1_2_9_34_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127417500468"},{"key":"e_1_2_9_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2013.08.018"},{"key":"e_1_2_9_36_2","doi-asserted-by":"publisher","DOI":"10.1134\/s1063776114030121"},{"key":"e_1_2_9_37_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-015-2067-4"},{"key":"e_1_2_9_38_2","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/7138971"},{"key":"e_1_2_9_39_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-015-2056-7"},{"key":"e_1_2_9_40_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127416501376"},{"key":"e_1_2_9_41_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3920-4"},{"key":"e_1_2_9_42_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijleo.2016.06.111"},{"key":"e_1_2_9_43_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2014.11.006"},{"key":"e_1_2_9_44_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3505-2"},{"key":"e_1_2_9_45_2","doi-asserted-by":"publisher","DOI":"10.1155\/2016\/4024836"},{"key":"e_1_2_9_46_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127416300342"},{"key":"e_1_2_9_47_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2009.10.052"},{"key":"e_1_2_9_48_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-010-9678-6"},{"key":"e_1_2_9_49_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2011.01.037"},{"key":"e_1_2_9_50_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2014.11.011"},{"key":"e_1_2_9_51_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-013-0856-1"},{"key":"e_1_2_9_52_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-013-1200-5"},{"key":"e_1_2_9_53_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406015179"},{"key":"e_1_2_9_54_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127410025387"},{"key":"e_1_2_9_55_2","doi-asserted-by":"publisher","DOI":"10.1109\/tcsi.2011.2180429"},{"key":"e_1_2_9_56_2","article-title":"Simplification of chaotic circuits with quadratic nonlinearity","volume":"69","author":"Wu J.","year":"2021","journal-title":"IEEE Transactions on Circuits and Systems II: Express Briefs"},{"key":"e_1_2_9_57_2","article-title":"Optimal phase control in a Remoissenet\u2013Peyrard substrate potential: numerical and analogical investigations","author":"Kengne R.","year":"2022","journal-title":"Indian Journal of Physics"},{"key":"e_1_2_9_58_2","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.97.123902"},{"key":"e_1_2_9_59_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.88.052908"},{"key":"e_1_2_9_60_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.84.016226"},{"key":"e_1_2_9_61_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.2374860"},{"key":"e_1_2_9_62_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-015-2204-0"},{"key":"e_1_2_9_63_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2018.03.040"},{"key":"e_1_2_9_64_2","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ac1a4c"},{"key":"e_1_2_9_65_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjb\/e2017-70470-8"},{"key":"e_1_2_9_66_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-014-1583-y"},{"key":"e_1_2_9_67_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.protcy.2016.05.139"},{"key":"e_1_2_9_68_2","doi-asserted-by":"publisher","DOI":"10.17485\/ijst\/v14i27.532"},{"key":"e_1_2_9_69_2","doi-asserted-by":"publisher","DOI":"10.1109\/tie.2022.3144592"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2022\/8362836","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/2022\/8362836","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2022\/8362836","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T21:15:59Z","timestamp":1769116559000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2022\/8362836"}},"subtitle":[],"editor":[{"given":"Mustafa Cagri","family":"Kutlu","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2022,1]]},"references-count":69,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["10.1155\/2022\/8362836"],"URL":"https:\/\/doi.org\/10.1155\/2022\/8362836","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1]]},"assertion":[{"value":"2022-02-18","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-04-23","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-05-16","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"8362836"}}