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Taxicab geometry in table of higher-order elements

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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.

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Notes

  1. Disk (also denoted as disc) [52] is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary.

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Acknowledgements

This work has been supported by the Czech Science Foundation under Grant No. 18-21608S. For research, the infrastructure of K217 Department, UD Brno, was also used.

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic

    Zdeněk Biolek, Dalibor Biolek, Viera Biolková & Zdeněk Kolka

  2. Faculty of Military Technologies, University of Defence, Brno, Czech Republic

    Zdeněk Biolek & Dalibor Biolek

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  1. Zdeněk Biolek
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Correspondence to Dalibor Biolek.

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Biolek, Z., Biolek, D., Biolková, V. et al. Taxicab geometry in table of higher-order elements. Nonlinear Dyn 98, 623–636 (2019). https://doi.org/10.1007/s11071-019-05218-9

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