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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...

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Detalles Bibliográficos
Autores principales: Biolek, Zdeněk, Biolek, Dalibor, Biolková, Viera, Kolka, Zdeněk
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
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.
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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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