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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 ( , ) 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....
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| Published in: | Entropy (Basel, Switzerland) Switzerland), 2020-04, Vol.22 (4), p.412 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c441t-db638918aa8ae20aad72c92bf7e6928b948e9615c4e8566de6f01b37928d86e43 |
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| cites | cdi_FETCH-LOGICAL-c441t-db638918aa8ae20aad72c92bf7e6928b948e9615c4e8566de6f01b37928d86e43 |
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| container_issue | 4 |
| container_start_page | 412 |
| container_title | Entropy (Basel, Switzerland) |
| container_volume | 22 |
| creator | Biolek, Zdeněk Biolek, Dalibor Biolková, Viera Kolka, Zdeněk |
| description | The paper studies the construction of the Hamiltonian for circuits built from the (
,
) 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. |
| doi_str_mv | 10.3390/e22040412 |
| format | article |
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,
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,
) 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.</description><subject>Chua’s table</subject><subject>constitutive relation</subject><subject>Hamiltonian</subject><subject>higher-order element</subject><subject>Lagrangian</subject><subject>memristor</subject><issn>1099-4300</issn><issn>1099-4300</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>DOA</sourceid><recordid>eNpVkc9O3DAQxq2qFdCFQ18A-QhSU_wvjn0pqla0uxISFzhbE2eya5TEYGdBPFb7IDxTQ5eu4DSjmU-_-UYfIV84-yalZWcoBFNMcfGBHHBmbaEkYx_f9Pvkc863jAkpuN4j-1IKo7nRB-R8EVZrTMVVajDRBfShG-MQYKBtTHQekt-EMdPHMK7pCX3-Tb_S5z_0lF502OMw5kPyqYUu49FrnZGbnxfX80VxefVrOf9xWXil-Fg0tZbGcgNgAAUDaCrhrajbCrUVprbKoNW89ApNqXWDumW8ltW0a4xGJWdkueU2EW7dXQo9pCcXIbh_g5hWDtIYfIdOyxKYUAraBpQXqq5qpWRrGQOhwPqJ9X3LutvUPTZ--iNB9w76fjOEtVvFB1eVXJvKToCTV0CK9xvMo-tD9th1MGDcZCeUNlJWpX3xfbqV-hRzTtjuznDmXsJzu_Am7fFbXzvl_7TkX-zVk3c</recordid><startdate>20200405</startdate><enddate>20200405</enddate><creator>Biolek, Zdeněk</creator><creator>Biolek, Dalibor</creator><creator>Biolková, Viera</creator><creator>Kolka, Zdeněk</creator><general>MDPI</general><general>MDPI AG</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>5PM</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0002-7607-6146</orcidid><orcidid>https://orcid.org/0000-0003-3055-4621</orcidid><orcidid>https://orcid.org/0000-0003-2589-2722</orcidid></search><sort><creationdate>20200405</creationdate><title>Higher-Order Hamiltonian for Circuits with ( α , β ) Elements</title><author>Biolek, Zdeněk ; Biolek, Dalibor ; Biolková, Viera ; Kolka, Zdeněk</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c441t-db638918aa8ae20aad72c92bf7e6928b948e9615c4e8566de6f01b37928d86e43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Chua’s table</topic><topic>constitutive relation</topic><topic>Hamiltonian</topic><topic>higher-order element</topic><topic>Lagrangian</topic><topic>memristor</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Biolek, Zdeněk</creatorcontrib><creatorcontrib>Biolek, Dalibor</creatorcontrib><creatorcontrib>Biolková, Viera</creatorcontrib><creatorcontrib>Kolka, Zdeněk</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Entropy (Basel, Switzerland)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Biolek, Zdeněk</au><au>Biolek, Dalibor</au><au>Biolková, Viera</au><au>Kolka, Zdeněk</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Higher-Order Hamiltonian for Circuits with ( α , β ) Elements</atitle><jtitle>Entropy (Basel, Switzerland)</jtitle><addtitle>Entropy (Basel)</addtitle><date>2020-04-05</date><risdate>2020</risdate><volume>22</volume><issue>4</issue><spage>412</spage><pages>412-</pages><issn>1099-4300</issn><eissn>1099-4300</eissn><abstract>The paper studies the construction of the Hamiltonian for circuits built from the (
,
) 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.</abstract><cop>Switzerland</cop><pub>MDPI</pub><pmid>33286186</pmid><doi>10.3390/e22040412</doi><orcidid>https://orcid.org/0000-0002-7607-6146</orcidid><orcidid>https://orcid.org/0000-0003-3055-4621</orcidid><orcidid>https://orcid.org/0000-0003-2589-2722</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1099-4300 |
| ispartof | Entropy (Basel, Switzerland), 2020-04, Vol.22 (4), p.412 |
| issn | 1099-4300 1099-4300 |
| language | eng |
| recordid | cdi_doaj_primary_oai_doaj_org_article_635a0244afda4c24b7b443f900a24a9c |
| source | Publicly Available Content Database; DOAJ Directory of Open Access Journals; PubMed Central |
| subjects | Chua’s table constitutive relation Hamiltonian higher-order element Lagrangian memristor |
| title | Higher-Order Hamiltonian for Circuits with ( α , β ) Elements |
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