Publication detail

Higher-Order Hamiltonian for Circuits with (alpha,beta) Elements

BIOLEK, Z. BIOLEK, D. BIOLKOVÁ, V. KOLKA, Z.

Original Title

Higher-Order Hamiltonian for Circuits with (alpha,beta) Elements

Type

journal article in Web of Science

Language

English

Original Abstract

The paper studies the construction of the Hamiltonian for circuits built from the (alpha,beta) elements of Chua’s periodic table. It starts from the Lagrange function, whose existence is limited to sigma-circuits, i.e., circuits built exclusively from elements located on a common sigma-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 S-circuits is designed and examined with the example of a nonlinear Pais–Uhlenbeck oscillator.

Keywords

higher-order element; constitutive relation; Hamiltonian; Lagrangian; Chua’s table; memristor; Euler-Lagrange equation

Authors

BIOLEK, Z.; BIOLEK, D.; BIOLKOVÁ, V.; KOLKA, Z.

Released

5. 4. 2020

Publisher

MDPI AG

Location

Basel, Switzerland

ISBN

1099-4300

Periodical

ENTROPY

Year of study

22

Number

4

State

Swiss Confederation

Pages from

1

Pages to

20

Pages count

20

URL

https://www.mdpi.com/1099-4300/22/4/412

Full text in the Digital Library

http://hdl.handle.net/11012/188176

BibTex

@article{BUT164146,
  author="Zdeněk {Biolek} and Dalibor {Biolek} and Viera {Biolková} and Zdeněk {Kolka}",
  title="Higher-Order Hamiltonian for Circuits with (alpha,beta) Elements",
  journal="ENTROPY",
  year="2020",
  volume="22",
  number="4",
  pages="1--20",
  doi="10.3390/e22040412",
  issn="1099-4300",
  url="https://www.mdpi.com/1099-4300/22/4/412"
}