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Open AccessArticle

Higher-Order Hamiltonian for Circuits with (α,β) Elements

1
Department of Microelectronics, Brno University of Technology, 616 00 Brno, Czech Republic
2
Department of Electrical Engineering, University of Defence, 662 10 Brno, Czech Republic
3
Department of Radio Electronics, Brno University of Technology, 616 00 Brno, Czech Republic
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(4), 412; https://doi.org/10.3390/e22040412
Received: 22 February 2020 / Revised: 29 March 2020 / Accepted: 2 April 2020 / Published: 5 April 2020
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. View Full-Text
Keywords: higher-order element; constitutive relation; Hamiltonian; Lagrangian; Chua’s table; memristor; Euler-Lagrange equation higher-order element; constitutive relation; Hamiltonian; Lagrangian; Chua’s table; memristor; Euler-Lagrange equation
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Biolek, Z.; Biolek, D.; Biolková, V.; Kolka, Z. Higher-Order Hamiltonian for Circuits with (α,β) Elements. Entropy 2020, 22, 412.

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