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Open AccessArticle

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

Department of Radio Electronics, Faculty of Electronical Engineering and Communications, Brno University of Technology, 616 00 Brno, Czech Republic
Entropy 2020, 22(4), 422; https://doi.org/10.3390/e22040422
Received: 22 March 2020 / Revised: 5 April 2020 / Accepted: 7 April 2020 / Published: 9 April 2020
This paper provides readers with three partial results that are mutually connected. Firstly, the gallery of the so-called constant phase elements (CPE) dedicated for the wideband applications is presented. CPEs are calculated for 9° (decimal orders) and 10° phase steps including ¼, ½, and ¾ orders, which are the most used mathematical orders between zero and one in practice. For each phase shift, all necessary numerical values to design fully passive RC ladder two-terminal circuits are provided. Individual CPEs are easily distinguishable because of a very high accuracy; maximal phase error is less than 1.5° in wide frequency range beginning with 3 Hz and ending with 1 MHz. Secondly, dynamics of ternary memory composed by a series connection of two resonant tunneling diodes is investigated and, consequently, a robust chaotic behavior is discovered and reported. Finally, CPEs are directly used for realization of fractional-order (FO) ternary memory as lumped chaotic oscillator. Existence of structurally stable strange attractors for different orders is proved, both by numerical analyzed and experimental measurement. View Full-Text
Keywords: approximate entropy; admittance function synthesis; constant phase element; chaotic oscillator; fractional-order; frequency response; ternary memory; zeroes and poles approximate entropy; admittance function synthesis; constant phase element; chaotic oscillator; fractional-order; frequency response; ternary memory; zeroes and poles
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Petrzela, J. Fractional-Order Chaotic Memory with Wideband Constant Phase Elements. Entropy 2020, 22, 422.

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