Nonlinear Dynamics

, Volume 98, Issue 1, pp 623–636 | Cite as

Taxicab geometry in table of higher-order elements

  • Zdeněk Biolek
  • Dalibor BiolekEmail author
  • Viera Biolková
  • Zdeněk Kolka
Original paper


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.


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



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.

Compliance with ethical standards

Conflicts of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Faculty of Electrical Engineering and CommunicationBrno University of TechnologyBrnoCzech Republic
  2. 2.Faculty of Military TechnologiesUniversity of DefenceBrnoCzech Republic

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