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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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2020-04, Vol.22 (4), p.412
Main Authors: Biolek, Zdeněk, Biolek, Dalibor, Biolková, Viera, Kolka, Zdeněk
Format: Article
Language:English
Subjects:
Chua’s table
constitutive relation
Hamiltonian
higher-order element
Lagrangian
memristor
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Summary: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.
ISSN:1099-4300
1099-4300
DOI:10.3390/e22040412