{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T03:25:51Z","timestamp":1762917951121,"version":"3.41.2"},"reference-count":34,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2018,11,7]],"date-time":"2018-11-07T00:00:00Z","timestamp":1541548800000},"content-version":"vor","delay-in-days":310,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","doi-asserted-by":"publisher","award":["18-21608S"],"award-info":[{"award-number":["18-21608S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>The duality of nonlinear systems built from higher\u2010order two\u2010terminal Chua\u2019s elements and independent voltage and current sources is analyzed. Two different approaches are now being generalized for circuits with higher\u2010order elements: the classical duality principle, hitherto restricted to circuits built from R\u2010C\u2010L elements, and Chua\u2019s duality of memristive circuits. The so\u2010called storeyed structure of fundamental elements is used as an integrating platform of both approaches. It is shown that the combination of associated flip\u2010type and shift\u2010type transformations of the circuit elements can generate dual networks with interesting features. The regularities of the duality can be used for modeling, hardware emulation, or synthesis of systems built from elements that are not commonly available, such as memristors, via classical dual elements.<\/jats:p>","DOI":"10.1155\/2018\/5719397","type":"journal-article","created":{"date-parts":[[2018,11,7]],"date-time":"2018-11-07T23:32:42Z","timestamp":1541633562000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Duality of Complex Systems Built from Higher\u2010Order Elements"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7607-6146","authenticated-orcid":false,"given":"Dalibor","family":"Biolek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3055-4621","authenticated-orcid":false,"given":"Zden\u011bk","family":"Biolek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2589-2722","authenticated-orcid":false,"given":"Viera","family":"Biolkov\u00e1","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,11,7]]},"reference":[{"volume-title":"A Treatise on the Theory of Alternating Currents","year":"1904","author":"Russell A.","key":"e_1_2_11_1_2"},{"volume-title":"Introductory Circuit Theory","year":"1953","author":"Guillemin E. A.","key":"e_1_2_11_2_2"},{"volume-title":"Analysis of Linear Systems","year":"1959","author":"Cheng D. K.","key":"e_1_2_11_3_2"},{"volume-title":"Modern Network Analysis","year":"1959","author":"Reza F. M.","key":"e_1_2_11_4_2"},{"volume-title":"Basic Circuit Theory","year":"1969","author":"Desoer C. A.","key":"e_1_2_11_5_2"},{"volume-title":"Network Theory","year":"1970","author":"Murdoch J. B.","key":"e_1_2_11_6_2"},{"volume-title":"Linear and Nonlinear Circuits","year":"1987","author":"Chua L. O.","key":"e_1_2_11_7_2"},{"key":"e_1_2_11_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1965.1082367"},{"key":"e_1_2_11_9_2","doi-asserted-by":"publisher","DOI":"10.1049\/el.2013.2788"},{"key":"e_1_2_11_10_2","doi-asserted-by":"publisher","DOI":"10.1049\/el.2014.1553"},{"key":"e_1_2_11_11_2","doi-asserted-by":"publisher","DOI":"10.1049\/el.2014.1963"},{"key":"e_1_2_11_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3952-9"},{"key":"e_1_2_11_13_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/5935637"},{"key":"e_1_2_11_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2017.10.001"},{"volume-title":"Theory of Nonlinear Networks and Systems","year":"1965","author":"Stern T. E.","key":"e_1_2_11_15_2"},{"key":"e_1_2_11_16_2","doi-asserted-by":"publisher","DOI":"10.1121\/1.1906947"},{"key":"e_1_2_11_17_2","doi-asserted-by":"publisher","DOI":"10.1515\/aee-2017-0050"},{"key":"e_1_2_11_18_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1969.1082989"},{"key":"e_1_2_11_19_2","doi-asserted-by":"crossref","unstructured":"ItohM.andChuaL. O. Duality of memristor circuits International Journal of Bifurcation and Chaos 2013 23 no. 1 article 1330001 https:\/\/doi.org\/10.1142\/S0218127413300012 2-s2.0-84874622288.","DOI":"10.1142\/S0218127413300012"},{"key":"e_1_2_11_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1980.1084742"},{"key":"e_1_2_11_21_2","doi-asserted-by":"publisher","DOI":"10.1049\/el.2016.2961"},{"key":"e_1_2_11_22_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/3872573"},{"key":"e_1_2_11_23_2","doi-asserted-by":"crossref","unstructured":"S\u00e1nchez-L\u00f3pezC. Carbajal-G\u00f3mezV. H. Carrasco-AguilarM. A. andCarro-P\u00e9rezI. Fractional-order memristor emulator circuits Complexity 2018 2018 10 2806976 https:\/\/doi.org\/10.1155\/2018\/2806976 2-s2.0-85048577949.","DOI":"10.1155\/2018\/2806976"},{"key":"e_1_2_11_24_2","doi-asserted-by":"crossref","unstructured":"MaundyB. J. ElwakilA. S. andPsychalinosC. CMOS realization of all-positive pinched hysteresis loops Complexity 2017 2017 15 7863095 https:\/\/doi.org\/10.1155\/2017\/7863095 2-s2.0-85028464061.","DOI":"10.1155\/2017\/7863095"},{"key":"e_1_2_11_25_2","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2003.818319"},{"key":"e_1_2_11_26_2","doi-asserted-by":"crossref","unstructured":"BiolekD. BiolekZ. andBiolkov\u00e1V. SPICE modeling of memristive memcapacitative and meminductive systems Proceedings of the European Conference on Circuit Theory and Design August 2009 Antalya Turkey 249\u2013252 https:\/\/doi.org\/10.1109\/ECCTD.2009.5274934 2-s2.0-71249130431.","DOI":"10.1109\/ECCTD.2009.5274934"},{"key":"e_1_2_11_27_2","doi-asserted-by":"publisher","DOI":"10.1109\/MCAS.2018.2821759"},{"key":"e_1_2_11_28_2","doi-asserted-by":"publisher","DOI":"10.13164\/re.2017.0397"},{"key":"e_1_2_11_29_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf02987158"},{"key":"e_1_2_11_30_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNANO.2018.2812359"},{"key":"e_1_2_11_31_2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2002.803532"},{"key":"e_1_2_11_32_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.84.132404"},{"key":"e_1_2_11_33_2","doi-asserted-by":"crossref","unstructured":"ZhaoY. ZhangB. HanF. TianH. YuX. andZhuJ. Instantaneous characteristics of nonlinear torsion pendulum and its application in parameter estimation of nonlinear system Mathematical Problems in Engineering 2018 2018 10 7858403 https:\/\/doi.org\/10.1155\/2018\/7858403 2-s2.0-85047630784.","DOI":"10.1155\/2018\/7858403"},{"key":"e_1_2_11_34_2","doi-asserted-by":"crossref","unstructured":"BiolekD. BiolekZ. andBiolkov\u00e1V. Memristors and other higher-order elements in generalized through-across domain Procceedings of the 2016 IEEE International Conference on Electronics Circuits and Systems (ICECS) December 2016 Monte Carlo Monaco 604\u2013607 https:\/\/doi.org\/10.1109\/ICECS.2016.7841274 2-s2.0-85015305745.","DOI":"10.1109\/ICECS.2016.7841274"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2018\/5719397.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2018\/5719397.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2018\/5719397","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T23:07:16Z","timestamp":1723158436000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2018\/5719397"}},"subtitle":[],"editor":[{"given":"Dan","family":"Seli\u015fteanu","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1155\/2018\/5719397"],"URL":"https:\/\/doi.org\/10.1155\/2018\/5719397","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2018,1]]},"assertion":[{"value":"2018-07-19","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-09-09","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-11-07","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"5719397"}}