{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T09:14:40Z","timestamp":1768036480058,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,5]],"date-time":"2020-04-05T00:00:00Z","timestamp":1586044800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/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":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The paper studies the construction of the Hamiltonian for circuits built from the (\u03b1,\u03b2) elements of Chua\u2019s periodic table. It starts from the Lagrange function, whose existence is limited to \u03a3-circuits, i.e., circuits built exclusively from elements located on a common \u03a3-diagonal of the table. We show that the Hamiltonian can also be constructed via the generalized Tellegen\u2019s theorem. According to the ideas of predictive modeling, the resulting Hamiltonian is made up exclusively of the constitutive relations of the elements in the circuit. Within the frame of Ostrogradsky\u2019s formalism, the simulation scheme of \u03a3-circuits is designed and examined with the example of a nonlinear Pais\u2013Uhlenbeck oscillator.<\/jats:p>","DOI":"10.3390\/e22040412","type":"journal-article","created":{"date-parts":[[2020,4,6]],"date-time":"2020-04-06T05:05:13Z","timestamp":1586149513000},"page":"412","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Higher-Order Hamiltonian for Circuits with (\u03b1,\u03b2) Elements"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3055-4621","authenticated-orcid":false,"given":"Zden\u011bk","family":"Biolek","sequence":"first","affiliation":[{"name":"Department of Microelectronics, Brno University of Technology, 616 00 Brno, Czech Republic"},{"name":"Department of Electrical Engineering, University of Defence, 662 10 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7607-6146","authenticated-orcid":false,"given":"Dalibor","family":"Biolek","sequence":"additional","affiliation":[{"name":"Department of Microelectronics, Brno University of Technology, 616 00 Brno, Czech Republic"},{"name":"Department of Electrical Engineering, University of Defence, 662 10 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2589-2722","authenticated-orcid":false,"given":"Viera","family":"Biolkov\u00e1","sequence":"additional","affiliation":[{"name":"Department of Radio Electronics, Brno University of Technology, 616 00 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zden\u011bk","family":"Kolka","sequence":"additional","affiliation":[{"name":"Department of Radio Electronics, Brno University of Technology, 616 00 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Fuchs, A. 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