Publication detail

# Taxicab geometry in table of higher-order elements

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

Original Title

Taxicab geometry in table of higher-order elements

English Title

Taxicab geometry in table of higher-order elements

Type

journal article in Web of Science

Language

en

Original Abstract

The paper deals with the analysis of the order of the differential equation of motion describing the dynamics of a one-port network compounded of series or parallel connections of arbitrary elements from Chua’s table. It takes advantage of the fact that the elements in the table are arranged in a square graticule, which conforms to the so-called taxicab geometry. The order of the equation of motion is then expressed via the so-called Manhattan metric, which is applied to measuring the distance between individual elements in the table. It is demonstrated that the order can be taken as the radius of the so-called quarter-circle. The quarter-circle is a geometric figure in Chua’s table, circumscribed around an imaginary central point where the so-called hidden element of the one-port network is located.

English abstract

The paper deals with the analysis of the order of the differential equation of motion describing the dynamics of a one-port network compounded of series or parallel connections of arbitrary elements from Chua’s table. It takes advantage of the fact that the elements in the table are arranged in a square graticule, which conforms to the so-called taxicab geometry. The order of the equation of motion is then expressed via the so-called Manhattan metric, which is applied to measuring the distance between individual elements in the table. It is demonstrated that the order can be taken as the radius of the so-called quarter-circle. The quarter-circle is a geometric figure in Chua’s table, circumscribed around an imaginary central point where the so-called hidden element of the one-port network is located.

Keywords

Higher-order elements; Chua’s table; Memristor; Complexity; Dimension; Equation of motion; Taxicab geometry; Manhattan metric

Released

30.08.2019

Publisher

Springer Nature

Location

USA

Pages from

623

Pages to

636

Pages count

14

URL

BibTex

```
@article{BUT158347,
author="Zdeněk {Biolek} and Dalibor {Biolek} and Viera {Biolková} and Zdeněk {Kolka}",
title="Taxicab geometry in table of higher-order elements",
annote="The paper deals with the analysis of the order of the differential equation of motion describing the dynamics of a one-port network compounded of series or parallel connections of arbitrary elements from Chua’s table. It takes advantage of the fact that the elements in the table are arranged in a square graticule, which conforms to the so-called taxicab geometry. The order of the equation of motion is then expressed via the so-called Manhattan metric, which is applied to measuring the distance between individual elements in the table. It is demonstrated that the order can be taken as the radius of the so-called quarter-circle. The quarter-circle is a geometric figure in Chua’s table, circumscribed around an imaginary central point where the so-called hidden element of the one-port network is located.",
address="Springer Nature",
chapter="158347",
doi="10.1007/s11071-019-05218-9",
howpublished="online",
institution="Springer Nature",
number="1",
volume="98",
year="2019",
month="august",
pages="623--636",
publisher="Springer Nature",
type="journal article in Web of Science"
}
```