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Higher-Order Hamiltonian for Circuits with (α,β) Elements
The paper studies the construction of the Hamiltonian for circuits built from the (α,β) elements of Chua’s periodic table. It starts from the Lagrange function, whose existence is limited to Σ-circuits, i.e., circuits built exclusively from elements located on a common Σ-diagonal of the table. We sh...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516879/ https://www.ncbi.nlm.nih.gov/pubmed/33286186 http://dx.doi.org/10.3390/e22040412 |
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author | Biolek, Zdeněk Biolek, Dalibor Biolková, Viera Kolka, Zdeněk |
author_facet | Biolek, Zdeněk Biolek, Dalibor Biolková, Viera Kolka, Zdeněk |
author_sort | Biolek, Zdeněk |
collection | PubMed |
description | The paper studies the construction of the Hamiltonian for circuits built from the (α,β) elements of Chua’s periodic table. It starts from the Lagrange function, whose existence is limited to Σ-circuits, i.e., circuits built exclusively from elements located on a common Σ-diagonal of the table. We show that the Hamiltonian can also be constructed via the generalized Tellegen’s 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’s formalism, the simulation scheme of Σ-circuits is designed and examined with the example of a nonlinear Pais–Uhlenbeck oscillator. |
format | Online Article Text |
id | pubmed-7516879 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75168792020-11-09 Higher-Order Hamiltonian for Circuits with (α,β) Elements Biolek, Zdeněk Biolek, Dalibor Biolková, Viera Kolka, Zdeněk Entropy (Basel) Article The paper studies the construction of the Hamiltonian for circuits built from the (α,β) elements of Chua’s periodic table. It starts from the Lagrange function, whose existence is limited to Σ-circuits, i.e., circuits built exclusively from elements located on a common Σ-diagonal of the table. We show that the Hamiltonian can also be constructed via the generalized Tellegen’s 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’s formalism, the simulation scheme of Σ-circuits is designed and examined with the example of a nonlinear Pais–Uhlenbeck oscillator. MDPI 2020-04-05 /pmc/articles/PMC7516879/ /pubmed/33286186 http://dx.doi.org/10.3390/e22040412 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Biolek, Zdeněk Biolek, Dalibor Biolková, Viera Kolka, Zdeněk Higher-Order Hamiltonian for Circuits with (α,β) Elements |
title | Higher-Order Hamiltonian for Circuits with (α,β) Elements |
title_full | Higher-Order Hamiltonian for Circuits with (α,β) Elements |
title_fullStr | Higher-Order Hamiltonian for Circuits with (α,β) Elements |
title_full_unstemmed | Higher-Order Hamiltonian for Circuits with (α,β) Elements |
title_short | Higher-Order Hamiltonian for Circuits with (α,β) Elements |
title_sort | higher-order hamiltonian for circuits with (α,β) elements |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516879/ https://www.ncbi.nlm.nih.gov/pubmed/33286186 http://dx.doi.org/10.3390/e22040412 |
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