Higher-Order Hamiltonian for Circuits with (<em>α</em>,<em>β</em>) Elements

Higher-Order Hamiltonian for Circuits with (<em>α</em>,<em>β</em>) Elements

The paper studies the construction of the Hamiltonian for circuits built from the (<em>α</em>,<em>β</em>) 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...

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Bibliographic Details
Main Authors: Zdeněk Biolek, Dalibor Biolek, Viera Biolková, Zdeněk Kolka
Format: Article
Language:English
Published: MDPI AG 2020-04-01
Series:Entropy
Subjects:
higher-order element
constitutive relation
Hamiltonian
Lagrangian
Chua’s table
memristor
Online Access:https://www.mdpi.com/1099-4300/22/4/412
id doaj-635a0244afda4c24b7b443f900a24a9c
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spelling doaj-635a0244afda4c24b7b443f900a24a9c2020-11-25T02:37:38ZengMDPI AGEntropy1099-43002020-04-012241241210.3390/e22040412Higher-Order Hamiltonian for Circuits with (<em>α</em>,<em>β</em>) ElementsZdeněk Biolek0Dalibor Biolek1Viera Biolková2Zdeněk Kolka3Department of Microelectronics, Brno University of Technology, 616 00 Brno, Czech RepublicDepartment of Microelectronics, Brno University of Technology, 616 00 Brno, Czech RepublicDepartment of Radio Electronics, Brno University of Technology, 616 00 Brno, Czech RepublicDepartment of Radio Electronics, Brno University of Technology, 616 00 Brno, Czech RepublicThe paper studies the construction of the Hamiltonian for circuits built from the (<em>α</em>,<em>β</em>) 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.https://www.mdpi.com/1099-4300/22/4/412higher-order elementconstitutive relationHamiltonianLagrangianChua’s tablememristor
collection DOAJ
language English
format Article
sources DOAJ
author Zdeněk Biolek
Dalibor Biolek
Viera Biolková
Zdeněk Kolka
spellingShingle Zdeněk Biolek
Dalibor Biolek
Viera Biolková
Zdeněk Kolka
Higher-Order Hamiltonian for Circuits with (<em>α</em>,<em>β</em>) Elements
Entropy
higher-order element
constitutive relation
Hamiltonian
Lagrangian
Chua’s table
memristor
author_facet Zdeněk Biolek
Dalibor Biolek
Viera Biolková
Zdeněk Kolka
author_sort Zdeněk Biolek
title Higher-Order Hamiltonian for Circuits with (<em>α</em>,<em>β</em>) Elements
title_short Higher-Order Hamiltonian for Circuits with (<em>α</em>,<em>β</em>) Elements
title_full Higher-Order Hamiltonian for Circuits with (<em>α</em>,<em>β</em>) Elements
title_fullStr Higher-Order Hamiltonian for Circuits with (<em>α</em>,<em>β</em>) Elements
title_full_unstemmed Higher-Order Hamiltonian for Circuits with (<em>α</em>,<em>β</em>) Elements
title_sort higher-order hamiltonian for circuits with (<em>α</em>,<em>β</em>) elements
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2020-04-01
description The paper studies the construction of the Hamiltonian for circuits built from the (<em>α</em>,<em>β</em>) 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.
topic higher-order element
constitutive relation
Hamiltonian
Lagrangian
Chua’s table
memristor
url https://www.mdpi.com/1099-4300/22/4/412
work_keys_str_mv AT zdenekbiolek higherorderhamiltonianforcircuitswithemaemembemelements
AT daliborbiolek higherorderhamiltonianforcircuitswithemaemembemelements
AT vierabiolkova higherorderhamiltonianforcircuitswithemaemembemelements
AT zdenekkolka higherorderhamiltonianforcircuitswithemaemembemelements
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