Affordable Access

deepdyve-link
Publisher Website

Multidimensional scaling locus of memristor and fractional order elements

Authors
  • Tenreiro Machado, J.A.1
  • Lopes, António M.2
  • 1 Institute of Engineering, Polytechnic of Porto, Dept. of Electrical Engineering, Porto, Portugal
  • 2 UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Porto, Portugal
Type
Published Article
Journal
Journal of Advanced Research
Publisher
Elsevier
Publication Date
Jan 20, 2020
Volume
25
Pages
147–157
Identifiers
DOI: 10.1016/j.jare.2020.01.004
PMID: 32922982
PMCID: PMC7474200
Source
PubMed Central
Keywords
License
Unknown

Abstract

This paper combines the synergies of three mathematical and computational generalizations. The concepts of fractional calculus, memristor and information visualization extend the classical ideas of integro-differential calculus, electrical elements and data representation, respectively. The study embeds these notions in a common framework, with the objective of organizing and describing the "continuum" of fractional order elements (FOE). Each FOE is characterized by its behavior, either in the time or in the frequency domains, and the differences between the FOE are captured by a variety of distinct indices, such as the Arccosine, Canberra, Jaccard and Sørensen distances. The dissimilarity information is processed by the multidimensional scaling (MDS) computational algorithm to unravel possible clusters and to allow a direct pattern visualization. The MDS yields 3-dimensional loci organized according to the FOE characteristics both for linear and nonlinear elements. The new representation generalizes the standard Cartesian 2-dimensional periodic table of elements.

Report this publication

Statistics

Seen <100 times