{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,11]],"date-time":"2024-07-11T18:38:41Z","timestamp":1720723121214},"reference-count":36,"publisher":"Wiley","issue":"11","license":[{"start":{"date-parts":[[2014,10,30]],"date-time":"2014-10-30T00:00:00Z","timestamp":1414627200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"crossref","award":["MTM2010-15102"],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuit Theory & Apps"],"published-print":{"date-parts":[[2015,11]]},"abstract":"Summary<\/jats:title>This paper presents a comprehensive taxonomy of so\u2010called second\u2010order memory devices, which include charge\u2010controlled memcapacitors and flux\u2010controlled meminductors, among other novel circuit elements. These devices, which are classified according to their differential and state orders, are necessary to get a complete extension of the family of classical nonlinear circuit elements (resistors, capacitors, and inductors) for all possible controlling variables. Using a fully nonlinear formalism, we obtain nondegeneracy conditions for a broad class of second\u2010order mem\u2010circuits. This class of circuits is expected to yield a rich dynamic behavior; in this regard, we explore certain bifurcation phenomena exhibited by a family of circuits including a charge\u2010controlled memcapacitor and a flux\u2010controlled meminductor, providing some directions for future research. Copyright \u00a9 2014 John Wiley & Sons, Ltd.<\/jats:p>","DOI":"10.1002\/cta.2037","type":"journal-article","created":{"date-parts":[[2014,10,30]],"date-time":"2014-10-30T11:27:13Z","timestamp":1414668433000},"page":"1719-1742","source":"Crossref","is-referenced-by-count":9,"title":["Second order mem\u2010circuits"],"prefix":"10.1002","volume":"43","author":[{"given":"Ricardo","family":"Riaza","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada a las Tecnolog\u00edas de la Informaci\u00f3n, ETSI Telecomunicaci\u00f3n Universidad Polit\u00e9cnica de Madrid Madrid Spain"}]}],"member":"311","published-online":{"date-parts":[[2014,10,30]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1038\/nature06932"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1049\/el.2013.2788"},{"key":"e_1_2_9_4_1","doi-asserted-by":"crossref","unstructured":"BiolekD BiolekZ BiolkovaV.SPICE modeling of memristive memcapacitive and meminductive systems.Proceedings of the European Conference Circuit Theory Design 2009;249\u2013252.","DOI":"10.1109\/ECCTD.2009.5274934"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/cta.1804"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2009.2021077"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408022354"},{"key":"e_1_2_9_8_1","article-title":"Global unique solvability for memristive circuit DAEs of index 1","author":"Jansen L","year":"2014","journal-title":"International Journal of Circuit Theory and Applications"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2011.2164169"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2009.0553"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127410025521"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127410027076"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1080\/00018732.2010.544961"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2011.2166369"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2012.2221174"},{"key":"e_1_2_9_16_1","doi-asserted-by":"crossref","unstructured":"TetzlaffR SchmidtT.Memristors and memristive circuits \u2010 An overview.Proceedings ISCAS'12 2012;1590\u20131595.","DOI":"10.1109\/ISCAS.2012.6271557"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-9068-5_5"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1971.1083337"},{"key":"e_1_2_9_19_1","first-page":"1830","article-title":"Nonlinear circuit foundations for nanodevices, Part I: The four\u2010element torus","volume":"19","author":"Chua LO","year":"2004","journal-title":"Proceedings of the IEEE"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2010.2097731"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1002\/cta.4490170207"},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.1002\/cta.4490170303"},{"key":"e_1_2_9_23_1","doi-asserted-by":"publisher","DOI":"10.1142\/6746"},{"key":"e_1_2_9_24_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1981.1084943"},{"key":"e_1_2_9_25_1","volume-title":"Linear and Nonlinear Circuits","author":"Chua LO","year":"1987"},{"key":"e_1_2_9_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/0016-0032(63)90534-9"},{"key":"e_1_2_9_27_1","volume-title":"Numerical Solution of Initial\u2010Value Problems in Differential\u2010Algebraic Equations","author":"Brenan KE","year":"1996"},{"key":"e_1_2_9_28_1","doi-asserted-by":"publisher","DOI":"10.4171\/017"},{"key":"e_1_2_9_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-27555-5"},{"key":"e_1_2_9_30_1","doi-asserted-by":"publisher","DOI":"10.1137\/100816559"},{"key":"e_1_2_9_31_1","volume-title":"The Theory of Matrices","author":"Gantmacher FR","year":"1959"},{"key":"e_1_2_9_32_1","doi-asserted-by":"publisher","DOI":"10.1137\/S089547989936457X"},{"key":"e_1_2_9_33_1","doi-asserted-by":"publisher","DOI":"10.1109\/9.478226"},{"key":"e_1_2_9_34_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0619-4"},{"key":"e_1_2_9_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/b100033"},{"key":"e_1_2_9_36_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0933-1"},{"key":"e_1_2_9_37_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1980.1084745"}],"container-title":["International Journal of Circuit Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcta.2037","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cta.2037","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T22:25:14Z","timestamp":1696631114000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cta.2037"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,30]]},"references-count":36,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2015,11]]}},"alternative-id":["10.1002\/cta.2037"],"URL":"https:\/\/doi.org\/10.1002\/cta.2037","archive":["Portico"],"relation":{},"ISSN":["0098-9886","1097-007X"],"issn-type":[{"value":"0098-9886","type":"print"},{"value":"1097-007X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,30]]}}}